Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling

PCA-based synthetic sensitivity coefficients for chemical reaction network in cancer

Chemical reaction networks are powerful tools for modeling cell signaling and its disruptions in diseases like cancer. Realistic chemical reaction networks involve hundreds of proteins and reactions, resulting in a model depending on a consistently large number of kinetic parameters. Since finely calibrating all the parameters would require an unrealistic amount of data, proper sensitivity analysis is required to identify a subset of parameters for which fine tuning is needed and thus provide a fundamental tool for the qualitative analysis of the network. We present a multidisciplinary approach for computing a set of synthetic sensitivity indices. These indices rank the kinetic parameters, based on the impact that errors in their values would have on the protein concentration profile at equilibrium. Our tests on a chemical reaction network devised for colorectal cells demonstrate the effectiveness of the considered sensitivity indices in different scenarios including in-silico drug dosage and novel therapeutic target discovery. The Matlab code for computing the synthetic sensitivity indices and the data concerning the network for colorectal cells are available at https://github.com/theMIDAgroup/CRN_sensitivity.

Index analysis: An approach to understand signal transduction with application to the EGFR signalling pathway

In systems biology and pharmacology, large-scale kinetic models are used to study the dynamic response of a system to a specific input or stimulus. While in many applications, a deeper understanding of the input-response behaviour is highly desirable, it is often hindered by the large number of molecular species and the complexity of the interactions. An approach that identifies key molecular species for a given input-response relationship and characterises dynamic properties of states is therefore highly desirable. We introduce the concept of index analysis; it is based on different time- and state-dependent quantities (indices) to identify important dynamic characteristics of molecular species. All indices are defined for a specific pair of input and response variables as well as for a specific magnitude of the input. In application to a large-scale kinetic model of the EGFR signalling cascade, we identified different phases of signal transduction, the peculiar role of Phosphatase3 during signal activation and Ras recycling during signal onset. In addition, we discuss the challenges and pitfalls of interpreting the relevance of molecular species based on knock-out simulation studies, and provide an alternative view on conflicting results on the importance of parallel EGFR downstream pathways. Beyond the applications in model interpretation, index analysis is envisioned to be a valuable tool in model reduction.

Traversing through the Mechanistic Event Analysis in IL-6 and IL-17 Signaling for a New Therapeutic Paradigm in NSCLC

IL-6 and IL-17 are paradoxical cytokines that progress inflammatory states in chronic diseases, including cancer. In lung cancer, their role has been elucidated to favor cancer development by modulating signaling mechanisms critical to cellular growth. The intrinsic ability of these cytokines to influence macroautophagy is yet another reason to facilitate lung cancer. Here, we employed a systems immunology approach to discover the mechanistic role of these cytokines in cancer development. In a biological system, at later stages, the activation of NFkB stimulates immunosuppressive phenotypes to achieve tolerating effects in a transformed cell. We found that the upregulation of cytokines signaled M2 macrophages to modulate tumor responses through the activation of autophagic intermediates and inflammasome mediators. This caused immune perturbations in the tumor microenvironment, which were associated with cancer inflammation. To address these inflammatory states, we performed triggered event analysis to examine whether overexpressing immune effectors or downregulating immune suppressors may have an effect on cancer reversal. Interestingly, the inhibition of immune regulators opposed the model outcome to an increased immune response. Therefore, IL6-IL17-mediated regulation of lung cancer may address tumor malignancy and potentiate the development of newer therapeutics for NSCLC.

MicroRNA-520c-3p impacts sphingolipid metabolism mediating PI3K/AKT signaling in NSCLC: Systems perspective

Increasing research suggests that sphingolipid metabolism is essential for the progression and metastasis of cancer. The underlying mechanistic insight into the dysregulation of sphingolipid metabolism affecting pathways is poorly investigated. As a result, the goal of the current study was to glean knowledge from the systems biology approach to investigate how the sphingolipid metabolism affects the signal transduction network in non-small cell lung cancer (NSCLC), the most common type of cancer in terms of occurrence and death globally. Our paper includes system-level models representing the diseased and healthy states elucidating that sphingolipids and its enzymes mediate PI3K/AKT pathway. Notably, its activation of downstream signaling mediators has led to cancer growth. Considering the critical role of sphingolipids in NSCLC, our study advocates the target CERS6 which can be potentially inhibited using hsa-miR-520c-3p to combat NSCLC for future precision medicine.

Computational System Level Approaches for Discerning Reciprocal Regulation of IL10 and IL12 in Leishmaniasis

IL12 and IL10 are two of the major cytokines which control the fate of Leishmaniasis. This paper presents two models healthy state and diseased state which shows how secretion of IL12 is responsible for parasite elimination and IL10 can jeopardize the parasite elimination and promote its survival. Epigenetic modification in the host IL12 and IL10 promoter can decide the fate of parasites. It was observed that reciprocal relationship exists between IL12 and IL10 and that is majorly controlled by a transcription factor NFAT5 from Rel family of transcription factors. By targeting this transcription factor at the cellular level, it might be possible to modulate the release of powerful pro-inflammatory cytokines, thereby reducing parasite survival. The mathematical models developed here serves as a step towards finding a key component that can pave a way for therapeutic investigation.

Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

Evaluating model reduction under parameter uncertainty

BACKGROUND

The dynamics of biochemical networks can be modelled by systems of ordinary differential equations. However, these networks are typically large and contain many parameters. Therefore model reduction procedures, such as lumping, sensitivity analysis and time-scale separation, are used to simplify models. Although there are many different model reduction procedures, the evaluation of reduced models is difficult and depends on the parameter values of the full model. There is a lack of a criteria for evaluating reduced models when the model parameters are uncertain.

RESULTS

We developed a method to compare reduced models and select the model that results in similar dynamics and uncertainty as the original model. We simulated different parameter sets from the assumed parameter distributions. Then, we compared all reduced models for all parameter sets using cluster analysis. The clusters revealed which of the reduced models that were similar to the original model in dynamics and variability. This allowed us to select the smallest reduced model that best approximated the full model. Through examples we showed that when parameter uncertainty was large, the model should be reduced further and when parameter uncertainty was small, models should not be reduced much.

CONCLUSIONS

A method to compare different models under parameter uncertainty is developed. It can be applied to any model reduction method. We also showed that the amount of parameter uncertainty influences the choice of reduced models.

Model reduction in mathematical pharmacology : Integration, reduction and linking of PBPK and systems biology models

In this paper we present a framework for the reduction and linking of physiologically based pharmacokinetic (PBPK) models with models of systems biology to describe the effects of drug administration across multiple scales. To address the issue of model complexity, we propose the reduction of each type of model separately prior to being linked. We highlight the use of balanced truncation in reducing the linear components of PBPK models, whilst proper lumping is shown to be efficient in reducing typically nonlinear systems biology type models. The overall methodology is demonstrated via two example systems; a model of bacterial chemotactic signalling in Escherichia coli and a model of extracellular regulatory kinase activation mediated via the extracellular growth factor and nerve growth factor receptor pathways. Each system is tested under the simulated administration of three hypothetical compounds; a strong base, a weak base, and an acid, mirroring the parameterisation of pindolol, midazolam, and thiopental, respectively. Our method can produce up to an 80% decrease in simulation time, allowing substantial speed-up for computationally intensive applications including parameter fitting or agent based modelling. The approach provides a straightforward means to construct simplified Quantitative Systems Pharmacology models that still provide significant insight into the mechanisms of drug action. Such a framework can potentially bridge pre-clinical and clinical modelling - providing an intermediate level of model granularity between classical, empirical approaches and mechanistic systems describing the molecular scale.

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.

A combined model reduction algorithm for controlled biochemical systems

BACKGROUND

Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest.

METHODS

In this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an 'averaged' lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of 'controlled' biochemical networks.

RESULTS

The algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system's input-output response even for highly complex networks.

CONCLUSIONS

Through application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation.

Functional aspects of the EGF-induced MAP kinase cascade: a complex self-organizing system approach

The EGF-induced MAP kinase cascade is one of the most important and best characterized networks in intracellular signalling. It has a vital role in the development and maturation of living organisms. However, when deregulated, it is involved in the onset of a number of diseases. Based on a computational model describing a "surface" and an "internalized" parallel route, we use systems biology techniques to characterize aspects of the network's functional organization. We examine the re-organization of protein groups from low to high external stimulation, define functional groups of proteins within the network, determine the parameter best encoding for input intensity and predict the effect of protein removal to the system's output response. Extensive functional re-organization of proteins is observed in the lower end of stimulus concentrations. As we move to higher concentrations the variability is less pronounced. 6 functional groups have emerged from a consensus clustering approach, reflecting different dynamical aspects of the network. Mutual information investigation revealed that the maximum activation rate of the two output proteins best encodes for stimulus intensity. Removal of each protein of the network resulted in a range of graded effects, from complete silencing to intense activation. Our results provide a new "vista" of the EGF-induced MAP kinase cascade, from the perspective of complex self-organizing systems. Functional grouping of the proteins reveals an organizational scheme contrasting the current understanding of modular topology. The six identified groups may provide the means to experimentally follow the dynamics of this complex network. Also, the vulnerability analysis approach may be used for the development of novel therapeutic targets in the context of personalized medicine.

A model reduction method for biochemical reaction networks

BACKGROUND

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.

RESULTS

We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.

CONCLUSIONS

The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.

A structural systems biology approach for quantifying the systemic consequences of missense mutations in proteins

Gauging the systemic effects of non-synonymous single nucleotide polymorphisms (nsSNPs) is an important topic in the pursuit of personalized medicine. However, it is a non-trivial task to understand how a change at the protein structure level eventually affects a cell's behavior. This is because complex information at both the protein and pathway level has to be integrated. Given that the idea of integrating both protein and pathway dynamics to estimate the systemic impact of missense mutations in proteins remains predominantly unexplored, we investigate the practicality of such an approach by formulating mathematical models and comparing them with experimental data to study missense mutations. We present two case studies: (1) interpreting systemic perturbation for mutations within the cell cycle control mechanisms (G2 to mitosis transition) for yeast; (2) phenotypic classification of neuron-related human diseases associated with mutations within the mitogen-activated protein kinase (MAPK) pathway. We show that the application of simplified mathematical models is feasible for understanding the effects of small sequence changes on cellular behavior. Furthermore, we show that the systemic impact of missense mutations can be effectively quantified as a combination of protein stability change and pathway perturbation.

Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: incorporating EGFR signaling pathway and angiogenesis

Background

The epidermal growth factor receptor (EGFR) signaling pathway and angiogenesis in brain cancer act as an engine for tumor initiation, expansion and response to therapy. Since the existing literature does not have any models that investigate the impact of both angiogenesis and molecular signaling pathways on treatment, we propose a novel multi-scale, agent-based computational model that includes both angiogenesis and EGFR modules to study the response of brain cancer under tyrosine kinase inhibitors (TKIs) treatment.

Results

The novel angiogenesis module integrated into the agent-based tumor model is based on a set of reaction–diffusion equations that describe the spatio-temporal evolution of the distributions of micro-environmental factors such as glucose, oxygen, TGFα, VEGF and fibronectin. These molecular species regulate tumor growth during angiogenesis. Each tumor cell is equipped with an EGFR signaling pathway linked to a cell-cycle pathway to determine its phenotype. EGFR TKIs are delivered through the blood vessels of tumor microvasculature and the response to treatment is studied.

Conclusions

Our simulations demonstrated that entire tumor growth profile is a collective behaviour of cells regulated by the EGFR signaling pathway and the cell cycle. We also found that angiogenesis has a dual effect under TKI treatment: on one hand, through neo-vasculature TKIs are delivered to decrease tumor invasion; on the other hand, the neo-vasculature can transport glucose and oxygen to tumor cells to maintain their metabolism, which results in an increase of cell survival rate in the late simulation stages.

A specialized ODE integrator for the efficient computation of parameter sensitivities

Background

Dynamic mathematical models in the form of systems of ordinary differential equations (ODEs) play an important role in systems biology. For any sufficiently complex model, the speed and accuracy of solving the ODEs by numerical integration is critical. This applies especially to systems identification problems where the parameter sensitivities must be integrated alongside the system variables. Although several very good general purpose ODE solvers exist, few of them compute the parameter sensitivities automatically.

Results

We present a novel integration algorithm that is based on second derivatives and contains other unique features such as improved error estimates. These features allow the integrator to take larger time steps than other methods. In practical applications, i.e. systems biology models of different sizes and behaviors, the method competes well with established integrators in solving the system equations, and it outperforms them significantly when local parameter sensitivities are evaluated. For ease-of-use, the solver is embedded in a framework that automatically generates the integrator input from an SBML description of the system of interest.

Conclusions

For future applications, comparatively ‘cheap’ parameter sensitivities will enable advances in solving large, otherwise computationally expensive parameter estimation and optimization problems. More generally, we argue that substantially better computational performance can be achieved by exploiting characteristics specific to the problem domain; elements of our methods such as the error estimation could find broader use in other, more general numerical algorithms.

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

Simulating EGFR-ERK signaling control by scaffold proteins KSR and MP1 reveals differential ligand-sensitivity co-regulated by Cbl-CIN85 and endophilin

ERK activation is enhanced by the scaffolding proteins KSR and MP1, localized near the cell membrane and late endosomes respectively, but little is known about their dynamic interplay. We develop here a mathematical model with ordinary differential equations to describe the dynamic activation of EGFR-ERK signaling under a conventional pathway without scaffolds, a KSR-scaffolded pathway, and an MP1-scaffolded pathway, and their impacts were examined under the influence of the endosomal regulators, Cbl-CIN85 and Endophilin A1. This new integrated model, validated against experimental results and computational constraints, shows that changes of ERK activation and EGFR endocytosis in response to EGF concentrations (i.e ligand sensitivity) depend on these scaffold proteins and regulators. The KSR-scaffolded and the conventional pathways act synergistically and are sensitive to EGF stimulation. When the KSR level is high, the sensitivity of ERK activation from this combined pathway remains low when Cbl-CIN85 level is low. But, such sensitivity can be increased with increasing levels of Endophilin if Cbl-CIN85 level becomes high. However, reduced KSR levels already present high sensitivity independent of Endophilin levels. In contrast, ERK activation by MP1 is additive to that of KSR but it shows little ligand-sensitivity under high levels of EGF. This can be partly reversed by increasing level of Endophilin while keeping Cbl-CIN85 level low. Further analyses showed that high levels of KSR affect ligand-sensitivity of EGFR endocytosis whereas MP1 ensures the robustness of endosomal ERK activation. These simulations constitute a multi-dimensional exploration of how EGF-dependent EGFR endocytosis and ERK activation are dynamically affected by scaffolds KSR and MP1, co-regulated by Cbl-CIN85 and Endophilin A1. Together, these results provide a detailed and quantitative demonstration of how regulators and scaffolds can collaborate to fine-tune the ligand-dependent sensitivity of EGFR endocytosis and ERK activation which could underlie differences during normal physiology, disease states and drug responses.

Reducing experimental variability in variance-based sensitivity analysis of biochemical reaction systems

Sensitivity analysis is a valuable task for assessing the effects of biological variability on cellular behavior. Available techniques require knowledge of nominal parameter values, which cannot be determined accurately due to experimental uncertainty typical to problems of systems biology. As a consequence, the practical use of existing sensitivity analysis techniques may be seriously hampered by the effects of unpredictable experimental variability. To address this problem, we propose here a probabilistic approach to sensitivity analysis of biochemical reaction systems that explicitly models experimental variability and effectively reduces the impact of this type of uncertainty on the results. The proposed approach employs a recently introduced variance-based method to sensitivity analysis of biochemical reaction systems [Zhang et al., J. Chem. Phys. 134, 094101 (2009)] and leads to a technique that can be effectively used to accommodate appreciable levels of experimental variability. We discuss three numerical techniques for evaluating the sensitivity indices associated with the new method, which include Monte Carlo estimation, derivative approximation, and dimensionality reduction based on orthonormal Hermite approximation. By employing a computational model of the epidermal growth factor receptor signaling pathway, we demonstrate that the proposed technique can greatly reduce the effect of experimental variability on variance-based sensitivity analysis results. We expect that, in cases of appreciable experimental variability, the new method can lead to substantial improvements over existing sensitivity analysis techniques.

Sensitivity analysis predicts that the ERK-pMEK interaction regulates ERK nuclear translocation

Following phosphorylation, nuclear translocation of the mitogen-activated protein kinases (MAPKs), ERK1 and ERK2, is critical for both gene expression and DNA replication induced by growth factors. ERK nuclear translocation has therefore been studied extensively, but many details remain unresolved, including whether or not ERK dimerisation is required for translocation. Here, we simulate ERK nuclear translocation with a compartmental computational model that includes systematic sensitivity analysis. The governing ordinary differential equations are solved with the backward differentiation formula and decoupled direct methods. To better understand the regulation of ERK nuclear translocation, we use this model in conjunction with a previously published model of the ERK pathway that does not include an ERK dimer species and with experimental measurements of nuclear translocation of wild-type ERK and a mutant form, ERK1-4, which is unable to dimerise. Sensitivity analysis reveals that the delayed nuclear uptake of ERK1-4 compared to that of wild-type ERK1 can be explained by the altered interaction of ERK1-4 with phosphorylated MEK (MAPK/ERK kinase), and so may be independent of dimerisation. Our study also identifies biological experiments that can verify this explanation.

Systems glycobiology: biochemical reaction networks regulating glycan structure and function

There is a growing use of bioinformatics based methods in the field of Glycobiology. These have been used largely to curate glycan structures, organize array-based experimental data and display existing knowledge of glycosylation-related pathways in silico. Although the cataloging of vast amounts of data is beneficial, it is often a challenge to gain meaningful mechanistic insight from this exercise alone. The development of specific analysis tools to query the database is necessary. If these queries can integrate existing knowledge of glycobiology, new insights may be gained. Such queries that couple biochemical knowledge and mathematics have been developed in the field of Systems Biology. The current review summarizes the current state of the art in the application of computational modeling in the field of Glycobiology. It provides (i) an overview of experimental and online resources that can be used to construct glycosylation reaction networks, (ii) mathematical methods to formulate the problem including a description of ordinary differential equation and logic-based reaction networks, (iii) optimization techniques that can be applied to fit experimental data for the purpose of model reconstruction and for evaluating unknown model parameters, (iv) post-simulation analysis methods that yield experimentally testable hypotheses and (v) a summary of available software tools that can be used by non-specialists to perform many of the above functions.

Task-oriented modular decomposition of biological networks: trigger mechanism in blood coagulation

Analysis of complex time-dependent biological networks is an important challenge in the current postgenomic era. We propose a middle-out approach for decomposition and analysis of complex time-dependent biological networks based on: 1), creation of a detailed mechanism-driven mathematical model of the network; 2), network response decomposition into several physiologically relevant subtasks; and 3), subsequent decomposition of the model, with the help of task-oriented necessity and sensitivity analysis into several modules that each control a single specific subtask, which is followed by further simplification employing temporal hierarchy reduction. The technique is tested and illustrated by studying blood coagulation. Five subtasks (threshold, triggering, control by blood flow velocity, spatial propagation, and localization), together with responsible modules, can be identified for the coagulation network. We show that the task of coagulation triggering is completely regulated by a two-step pathway containing a single positive feedback of factor V activation by thrombin. These theoretical predictions are experimentally confirmed by studies of fibrin generation in normal, factor V-, and factor VIII-deficient plasmas. The function of the factor V-dependent feedback is to minimize temporal and parametrical intervals of fibrin clot instability. We speculate that this pathway serves to lessen possibility of fibrin clot disruption by flow and subsequent thromboembolism.

Probabilistic sensitivity analysis of biochemical reaction systems

Sensitivity analysis is an indispensable tool for studying the robustness and fragility properties of biochemical reaction systems as well as for designing optimal approaches for selective perturbation and intervention. Deterministic sensitivity analysis techniques, using derivatives of the system response, have been extensively used in the literature. However, these techniques suffer from several drawbacks, which must be carefully considered before using them in problems of systems biology. We develop here a probabilistic approach to sensitivity analysis of biochemical reaction systems. The proposed technique employs a biophysically derived model for parameter fluctuations and, by using a recently suggested variance-based approach to sensitivity analysis [Saltelli et al., Chem. Rev. (Washington, D.C.) 105, 2811 (2005)], it leads to a powerful sensitivity analysis methodology for biochemical reaction systems. The approach presented in this paper addresses many problems associated with derivative-based sensitivity analysis techniques. Most importantly, it produces thermodynamically consistent sensitivity analysis results, can easily accommodate appreciable parameter variations, and allows for systematic investigation of high-order interaction effects. By employing a computational model of the mitogen-activated protein kinase signaling cascade, we demonstrate that our approach is well suited for sensitivity analysis of biochemical reaction systems and can produce a wealth of information about the sensitivity properties of such systems. The price to be paid, however, is a substantial increase in computational complexity over derivative-based techniques, which must be effectively addressed in order to make the proposed approach to sensitivity analysis more practical.

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

Background

The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is orchestrated. One of the reasons for the complexity of this pathway is the extensive network of inter-connected components involved in the signaling. In the aim of identifying critical mechanisms controlling signal transduction we have performed extensive analysis of an executable model of the EGFR pathway using the stochastic pi-calculus as a modeling language.

Results

Our analysis, done through simulation of various perturbations, suggests that the EGFR pathway contains regions of functional redundancy in the upstream parts; in the event of low EGF stimulus or partial system failure, this redundancy helps to maintain functional robustness. Downstream parts, like the parts controlling Ras and ERK, have fewer redundancies, and more than 50% inhibition of specific reactions in those parts greatly attenuates signal response. In addition, we suggest an abstract model that captures the main control mechanisms in the pathway. Simulation of this abstract model suggests that without redundancies in the upstream modules, signal transduction through the entire pathway could be attenuated. In terms of specific control mechanisms, we have identified positive feedback loops whose role is to prolong the active state of key components (e.g., MEK-PP, Ras-GTP), and negative feedback loops that help promote signal adaptation and stabilization.

Conclusions

The insights gained from simulating this executable model facilitate the formulation of specific hypotheses regarding the control mechanisms of the EGFR signaling, and further substantiate the benefit to construct abstract executable models of large complex biological networks.

Sensitivity analysis: from model parameters to system behaviour

Sensitivity analysis addresses the manner in which model behaviour depends on model parametrization. Global sensitivity analysis makes use of statistical tools to address system behaviour over a wide range of operating conditions, whereas local sensitivity analysis focuses attention on a specific set of nominal parameter values. This narrow focus allows a complete analytical treatment and straightforward interpretation in the local case. Sensitivity analysis is a valuable tool for model construction and interpretation, and can be applied in medicine and biotechnology to predict the effect of interventions.

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.

Systems-level modeling of cellular glycosylation reaction networks: O-linked glycan formation on natural selectin ligands

MOTIVATION

The emerging field of Glycomics requires the development of systems-based modeling strategies to relate glycosyltransferase gene expression and enzyme activity with carbohydrate structure and function.

RESULTS

We describe the application of object oriented programming concepts to define glycans, enzymes, reactions, pathways and compartments for modeling cellular glycosylation reaction networks. These class definitions are combined with current biochemical knowledge to define potential reaction networks that participate in the formation of the sialyl Lewis-X (sLe(X)) epitope on O-glycans linked to a leukocyte cell-surface glycoprotein, P-selectin Glycoprotein Ligand-1 (PSGL-1). Subset modeling, hierarchical clustering, principal component analysis and adjoint sensitivity analysis are applied to refine the reaction network and to quantify individual glycosyltransferase rate constants. Wet-lab experiments validate estimates from computer modeling. Such analysis predicts that sLe(X) expression varies directly with sialyltransferase alpha2,3ST3Gal-IV expression and inversely with alpha2,3ST3Gal-I/II.

AVAILABILITY

SBML files for all converged models are available at http://www.eng.buffalo.edu/~neel/bio_reaction_network.html

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.

How does a cell know what type of cell it is supposed to become? How do external chemical signals change the underlying “state” of the cell? How are response pathways triggered on the application of a stress? Such questions of differentiation, signal transduction, and stress response, while seemingly diverse, all pertain to the storage of state information, or “memory,” by biochemical switches. Just as a computer memory unit can store a bit of 0 or 1 through electrical signals, a biochemical switch can be in one of two states, where chemical signals are on or off. This lets the cell record the presence/absence of an environmental stimulus, the level of a signaling molecule, or the result of a cell fate decision. There are a small number of published ways by which a group of chemical reactions come together to realize a switch. We undertook an exhaustive computational exploration to see if chemical switches are indeed rare and found, surprisingly, that they are actually abundant, highly diverse, but related to one another. Our catalog of switches opens up new bioinformatics approaches to understanding cellular decision making and cellular memory.

Cross-scale sensitivity analysis of a non-small cell lung cancer model: linking molecular signaling properties to cellular behavior

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a two-dimensional, multiscale non-small cell lung cancer (NSCLC) model, we examine the effects of perturbations in system parameters which span both molecular and cellular levels, i.e. across scales of interest. This is achieved by first linking molecular and cellular activities and then assessing the influence of parameters at the molecular level on the tumor's spatio-temporal expansion rate, which serves as the output behavior at the cellular level. Overall, the algorithm operated reliably over relatively large variations of most parameters, hence confirming the robustness of the model. However, three pathway components (proteins PKC, MEK, and ERK) and eleven reaction steps were determined to be of critical importance by employing a sensitivity coefficient as an evaluation index. Each of these sensitive parameters exhibited a similar changing pattern in that a relatively larger increase or decrease in its value resulted in a lesser influence on the system's cellular performance. This study provides a novel cross-scaled approach to analyzing sensitivities of computational model parameters and proposes its application to interdisciplinary biomarker studies.

In silico Biochemical Reaction Network Analysis (IBRENA): a package for simulation and analysis of reaction networks

SUMMARY

We present In silico Biochemical Reaction Network Analysis (IBRENA), a software package which facilitates multiple functions including cellular reaction network simulation and sensitivity analysis (both forward and adjoint methods), coupled with principal component analysis, singular-value decomposition and model reduction. The software features a graphical user interface that aids simulation and plotting of in silico results. While the primary focus is to aid formulation, testing and reduction of theoretical biochemical reaction networks, the program can also be used for analysis of high-throughput genomic and proteomic data.

AVAILABILITY

The software package, manual and examples are available at http://www.eng.buffalo.edu/~neel/ibrena

Neuronal firing sensitivity to morphologic and active membrane parameters

Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

Homeostasis is a process that allows a system to maintain a certain level of output over a long time, even though the inputs controlling the output are changing. Recently, studies of neurons and neuronal networks have shown that the “active” parameters that describe the movement of ions across the cell membrane contribute to homeostasis, since these parameters can be combined in different ways to maintain a specific output. There is also evidence that the physical shape (“morphology”) of the neuron may play a role in homeostasis, but this possibility has not been explored in computational models. We have developed a method that uses sensitivity analysis to evaluate how different kinds of parameters, like active and morphologic ones, affect model output. Across a multi-dimensional parameter space, we identified both local and global trends in parameter sensitivities that indicate regions where different parameters, even morphologic ones, contribute strongly to homeostasis. Significantly, the authors used sensitivities to predict which parameters should change, and by how much, to compensate for changes in another parameter to restore normal function. These predictions may prove important to neuronal aging, disease, and trauma research, but the method can be used to analyze any computational model.

The impact of the regulatory design on the response of epidermal growth factor receptor-mediated signal transduction towards oncogenic mutations

Epidermal growth factor receptor (EGFR)-mediated signal transduction is often hyperactivated in tumour cells and therefore considered a promising target for cancer therapy. A number of computational models have been developed which describe the pathway in great detail. These models are similar in their description of the activation events. The deactivation of the EGFR signalling seems to be cell type-specific and is less understood. Deactivation via receptor internalization, feedback inhibition of son of sevenless (SOS) by double phosphorylated, extracellular signal-regulated kinase (ERKPP) or transiently activated Ras-GTPase activating protein (Ras-GAP) proteins is discussed to play a role. In this study we address the question of to what extent the effect of oncogenic perturbations on EGFR signalling depend on the specific regulation structure. This is investigated using a detailed pathway model under two regulatory modes: the negative feedback via ERKPP to SOS and feed-forward deactivation via transiently activated Ras-GAP proteins. We show that the effect of receptor overexpression differs qualitatively under both regulations. In the system with transiently activated Ras-GAP it may result in an attenuation of the ERK activation. Such a nonintuitive effect was also observed experimentally. In general we find the model with transiently activated Ras-GAP to have a higher robustness towards receptor overexpression and Ras mutations. In particular, we demonstrate that this model can compensate for these oncogenic perturbations if the regulation is strong. The negative feedback can not protect the system against Ras mutations. A general sensitivity analysis, however, shows a higher robustness of the model under negative feedback, indicating the limited significance of such analyses for the prediction of specific oncogenic perturbations.

Integrin trafficking and its role in cancer metastasis

Enhanced levels of expression of certain integrins, and a consequent increase in specific integrin signals, have been linked to cancer cell progression. Dysfunctional integrin signaling is thought to be involved, at least in part, in mediating the detachment of tumor cells from neighboring cells while providing enhanced survival and proliferative capabilities which allow such disseminating tumor cells to grow in new, foreign, microenvironments. Cell biologists have known for some time that integrin heterodimers are endocytosed from the plasma membrane in to the cytoplasm with some of this receptor later being exocytosed back to the cell surface; a cellular mechanism referred to as 'trafficking'. Although extensive research within the integrin field has elucidated key signal transduction pathways as being involved in integrin-mediated cellular behavior, both in normal and transformed cells, it is only relatively recently that the importance of integrin trafficking in modulating cellular function has been demonstrated. This review aims to identify the major trafficking molecules found to play a functional role in cancer cell behavior with special emphasis on the importance of integrin trafficking during neoplastic cell migration and invasion; vital components of the metastatic process.

Signaling on the endocytic pathway

Endocytosis regulates many cellular signaling processes by controlling the number of functional receptors available at the cell surface. Conversely, some signaling processes regulate the endocytic pathway. Furthermore, various cellular signaling events appear to occur on endosome membranes. The endocytic pathway, by providing a set of dynamic and biochemically specialized endomembrane structures that physically communicate with the plasma membrane, is increasingly viewed as a highly flexible scaffold for mediating precise spatiotemporal control and transport of diverse biological signals. General principles of endosome-based signaling are beginning to emerge but, in many cases, the physiological significance of signaling on the endocytic pathway remains poorly understood.

Parametric analysis of metabolic fluxes of alpha-amylase and protease-producing Bacillus subtilis

Parametric analysis was applied for a metabolic flux model for the fed-batch culture of Bacillus subtilis producing recombinant alpha-amylase and protease. The metabolic flux model was formulated as a linear programming problem consisting of 49 reactions (decision variables) and 50 metabolites (equality constraints). This study was aimed to determine the response of the metabolic fluxes and objective function value of minimizing the difference between ATP consumption and ATP production (ATP balance). With regard to intracellular metabolite accumulation, the objective function value was least sensitive to variation in succinate and most sensitive to variation in malate. Amongst the variations in the accumulation rates of extracellular metabolites, the objective function value was least sensitive to variation in glutamate and most sensitive to variation in starch hydrolysis and triglyceride synthesis. A 10% variation in metabolite accumulation rates caused a maximum of 13.8% variation (standard error = 3.8%) in the objective function value.

Thermodynamically feasible kinetic models of reaction networks

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.

Data-driven modelling of signal-transduction networks

New technologies are permitting large-scale quantitative studies of signal-transduction networks. Such data are hard to understand completely by inspection and intuition. 'Data-driven models' help users to analyse large data sets by simplifying the measurements themselves. Data-driven modelling approaches such as clustering, principal components analysis and partial least squares can derive biological insights from large-scale experiments. These models are emerging as standard tools for systems-level research in signalling networks.

Endocytosis conducts the cell signaling orchestra

Endocytosis is used by eukaryotic cells to regulate nutrient internalization, signal transduction, and the composition of the plasma membrane. However, a more complex picture is emerging, in which endocytic pathways integrate diverse signals, thereby contributing to a higher level of cellular and organismal organization. In this way, endocytosis and cell signaling are intertwined in many biological processes, such as cell motility and cell fate determination.

Modeling the effects of HER/ErbB1-3 coexpression on receptor dimerization and biological response

The human epidermal growth factor receptor (HER/ErbB) system comprises the epidermal growth factor receptor (EGFR/HER1) and three other homologs, namely HERs 2-4. This receptor system plays a critical role in cell proliferation and differentiation and receptor overexpression has been associated with poor prognosis in cancers of the epithelium. Here, we examine the effect of coexpressing varying levels of HERs 1-3 on the receptor dimerization patterns using a detailed kinetic model for HER/ErbB dimerization and trafficking. Our results indicate that coexpression of EGFR with HER2 or HER3 biases signaling to the cell surface and retards signal downregulation. In addition, simultaneous coexpression of HERs 1-3 leads to an abundance of HER2-HER3 heterodimers, which are known to be potent inducers of cell growth and transformation. Our new approach to use parameter dependence analysis in experimental design reveals that measurements of HER3 phosphorylation and HER2 internalization ratio may prove to be especially useful for the estimation of critical model parameters. Further, we examine the effect of receptor dimerization patterns on biological response using a simple phenomenological model. Results indicate that coexpression of EGFR with HER2 and HER3 at low to moderate levels may enable cells to match the response of a high HER2 expresser.

Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway

The MAPK (mitogen-activated protein kinase) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular-signalling network that governs the growth, proliferation, differentiation and survival of many, if not all, cell types. It is de-regulated in various diseases, ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable, and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In the present review we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focusing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.

Current challenges in quantitative modeling of epidermal growth factor signaling

Over the last decade, epidermal growth factor (EGF) signaling has been used repeatedly as a test-bed for pioneering computational systems biology. Recent breakthroughs in our molecular understanding of EGF signaling pose new challenges for mathematical modeling strategies. Three key areas emerge as particularly relevant: the pervasive importance of compartmentalization and endosomal trafficking; the complexity of signalosome complexes; and the regulatory influence of diffusion and spatiality. Each one of them demands a drastic change in current computational approaches. We discuss recent developments in the field that address these emerging aspects in a new generation of more realistic - and potential more useful - models of EGF signaling.

A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity

We consider a model of early events in signaling by the epidermal growth factor (EGF) receptor (EGFR). The model includes EGF, EGFR, the adapter proteins Grb2 and Shc, and the guanine nucleotide exchange factor Sos, which is activated through EGF-induced formation of EGFR-Grb2-Sos and EGFR-Shc-Grb2-Sos assemblies at the plasma membrane. The protein interactions involved in signaling can potentially generate a diversity of protein complexes and phosphoforms; however, this diversity has been largely ignored in models of EGFR signaling. Here, we develop a model that accounts more fully for potential molecular diversity by specifying rules for protein interactions and then using these rules to generate a reaction network that includes all chemical species and reactions implied by the protein interactions. We obtain a model that predicts the dynamics of 356 molecular species, which are connected through 3749 unidirectional reactions. This network model is compared with a previously developed model that includes only 18 chemical species but incorporates the same scope of protein interactions. The predictions of this model are reproduced by the network model, which also yields new predictions. For example, the network model predicts distinct temporal patterns of autophosphorylation for different tyrosine residues of EGFR. A comparison of the two models suggests experiments that could lead to mechanistic insights about competition among adapter proteins for EGFR binding sites and the role of EGFR monomers in signal transduction.