Understanding complex signaling networks through models and metaphors

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

HillTau: A fast, compact abstraction for model reduction in biochemical signaling networks

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.

Chemical signals mediate many computations in cells, from housekeeping functions in all cells to memory and pattern selectivity in neurons. These signals form complex networks of interactions. Computer models are a powerful way to study how such networks behave, but it is hard to get all the chemical details for typical models, and it is slow to run them with standard numerical approaches to chemical kinetics. We introduce HillTau as a simplified way to model complex chemical networks. HillTau models condense multiple reaction steps into single steps defined by a small number of parameters for activation and settling time. As a result the models are simple, easy to find values for, and they run quickly. Remarkably, they fit the full chemical formulations rather well. We illustrate the utility of HillTau for modeling several signaling network functions, and for fitting complicated signaling networks.

Context-specific network modeling identifies new crosstalk in β-adrenergic cardiac hypertrophy

Cardiac hypertrophy is a context-dependent phenomenon wherein a myriad of biochemical and biomechanical factors regulate myocardial growth through a complex large-scale signaling network. Although numerous studies have investigated hypertrophic signaling pathways, less is known about hypertrophy signaling as a whole network and how this network acts in a context-dependent manner. Here, we developed a systematic approach, CLASSED (Context-specific Logic-bASed Signaling nEtwork Development), to revise a large-scale signaling model based on context-specific data and identify main reactions and new crosstalks regulating context-specific response. CLASSED involves four sequential stages with an automated validation module as a core which builds a logic-based ODE model from the interaction graph and outputs the model validation percent. The context-specific model is developed by estimation of default parameters, classified qualitative validation, hybrid Morris-Sobol global sensitivity analysis, and discovery of missing context-dependent crosstalks. Applying this pipeline to our prior-knowledge hypertrophy network with context-specific data revealed key signaling reactions which distinctly regulate cell response to isoproterenol, phenylephrine, angiotensin II and stretch. Furthermore, with CLASSED we developed a context-specific model of β-adrenergic cardiac hypertrophy. The model predicted new crosstalks between calcium/calmodulin-dependent pathways and upstream signaling of Ras in the ISO-specific context. Experiments in cardiomyocytes validated the model’s predictions on the role of CaMKII-Gβγ and CaN-Gβγ interactions in mediating hypertrophic signals in ISO-specific context and revealed a difference in the phosphorylation magnitude and translocation of ERK1/2 between cardiac myocytes and fibroblasts. CLASSED is a systematic approach for developing context-specific large-scale signaling networks, yielding insights into new-found crosstalks in β-adrenergic cardiac hypertrophy.

Pathological cardiac hypertrophy is a disease in which the heart grows abnormally in response to different motivators such as high blood pressure or variations in hormones and growth factors. The shape of the heart after its growth depends on the context in which it grows. Since cell signaling in the cardiac cells plays a key role in the determination of heart shape, a thorough understanding of cardiac cells signaling in each context enlightens the mechanisms which control response of cardiac cells. However, cell signaling in cardiac hypertrophy comprises a complex web of pathways with numerous interactions, and predicting how these interactions control the hypertrophic signal in each context is not achievable by only experiments or general computational models. To address this need, we developed an approach to bring together the experimental data of each context with a signaling network curated from literature to identify the main players of cardiac cells response in each context and attain the context-specific models of cardiac hypertrophy. By utilizing our approach, we identified the main regulators of cardiac hypertrophy in four important contexts. We developed a network model of β-adrenergic cardiac hypertrophy, and predicted and validated new interactions that regulate cardiac cells response in this context.

Michaelis-Menten dynamics in protein subnetworks

To understand the behaviour of complex systems, it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe, e.g., enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension, we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain a description of subnetwork dynamics, including memory functions, starting directly from any given network of unary, binary, and Michaelis-Menten reactions. Numerical tests show that this closed form enzyme elimination gives a much more accurate description of the subnetwork dynamics than the simpler method that represents enzymes explicitly and is also more efficient computationally.

Multiscale model of dynamic neuromodulation integrating neuropeptide-induced signaling pathway activity with membrane electrophysiology

We developed a multiscale model to bridge neuropeptide receptor-activated signaling pathway activity with membrane electrophysiology. Typically, the neuromodulation of biochemical signaling and biophysics have been investigated separately in modeling studies. We studied the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. Experiments have shown that AngII binding to the AngII receptor type-1 elicits baseline-dependent regulation of cytosolic Ca(2+) signaling. Our model simulations revealed a baseline Ca(2+)-dependent response to AngII receptor type-1 activation by AngII. Consistent with experimental observations, AngII evoked a rise in Ca(2+) when starting at a low baseline Ca(2+) level, and a decrease in Ca(2+) when starting at a higher baseline. Our analysis predicted that the kinetics of Ca(2+) transport into the endoplasmic reticulum play a critical role in shaping the Ca(2+) response. The Ca(2+) baseline also influenced the AngII-induced excitability changes such that lower Ca(2+) levels were associated with a larger firing rate increase. We examined the relative contributions of signaling kinases protein kinase C and Ca(2+)/Calmodulin-dependent protein kinase II to AngII-mediated excitability changes by simulating activity blockade individually and in combination. We found that protein kinase C selectively controlled firing rate adaptation whereas Ca(2+)/Calmodulin-dependent protein kinase II induced a delayed effect on the firing rate increase. We tested whether signaling kinetics were necessary for the dynamic effects of AngII on excitability by simulating three scenarios of AngII-mediated KDR channel phosphorylation: (1), an increased steady state; (2), a step-change increase; and (3), dynamic modulation. Our results revealed that the kinetics emerging from neuromodulatory activation of the signaling network were required to account for the dynamical changes in excitability. In summary, our integrated multiscale model provides, to our knowledge, a new approach for quantitative investigation of neuromodulatory effects on signaling and electrophysiology.

Memory effects in biochemical networks as the natural counterpart of extrinsic noise

We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. We use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation. Remarkably, in the limit of low intrinsic copy-number noise such expressions can be obtained even for nonlinear dependences on the past. We illustrate the method with examples from a protein interaction network around epidermal growth factor receptor (EGFR), which is relevant to cancer signalling. These examples demonstrate that inclusion of memory terms is not only important conceptually but also leads to substantially higher quantitative accuracy in the predicted subnetwork dynamics.

Mapping network motif tunability and robustness in the design of synthetic signaling circuits

Cellular networks are highly dynamic in their function, yet evolutionarily conserved in their core network motifs or topologies. Understanding functional tunability and robustness of network motifs to small perturbations in function and structure is vital to our ability to synthesize controllable circuits. In establishing core sets of network motifs, we selected topologies that are overrepresented in mammalian networks, including the linear, feedback, feed-forward, and bifan circuits. Static and dynamic tunability of network motifs were defined as the motif ability to respectively attain steady-state or transient outputs in response to pre-defined input stimuli. Detailed computational analysis suggested that static tunability is insensitive to the circuit topology, since all of the motifs displayed similar ability to attain predefined steady-state outputs in response to constant inputs. Dynamic tunability, in contrast, was tightly dependent on circuit topology, with some motifs performing superiorly in achieving observed time-course outputs. Finally, we mapped dynamic tunability onto motif topologies to determine robustness of motif structures to changes in topology and identify design principles for the rational assembly of robust synthetic networks.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain's long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways.

A network diffusion model of disease progression in dementia

Patterns of dementia are known to fall into dissociated but dispersed brain networks, suggesting that the disease is transmitted along neuronal pathways rather than by proximity. This view is supported by neuropathological evidence for "prion-like" transsynaptic transmission of disease agents like misfolded tau and beta amyloid. We mathematically model this transmission by a diffusive mechanism mediated by the brain's connectivity network obtained from tractography of 14 healthy-brain MRIs. Subsequent graph theoretic analysis provides a fully quantitative, testable, predictive model of dementia. Specifically, we predict spatially distinct "persistent modes," which, we found, recapitulate known patterns of dementia and match recent reports of selectively vulnerable dissociated brain networks. Model predictions also closely match T1-weighted MRI volumetrics of 18 Alzheimer's and 18 frontotemporal dementia subjects. Prevalence rates predicted by the model strongly agree with published data. This work has many important implications, including dimensionality reduction, differential diagnosis, and especially prediction of future atrophy using baseline MRI morphometrics.

Charting the NF-κB pathway interactome map

Inflammation is part of a complex physiological response to harmful stimuli and pathogenic stress. The five components of the Nuclear Factor κB (NF-κB) family are prominent mediators of inflammation, acting as key transcriptional regulators of hundreds of genes. Several signaling pathways activated by diverse stimuli converge on NF-κB activation, resulting in a regulatory system characterized by high complexity. It is increasingly recognized that the number of components that impinges upon phenotypic outcomes of signal transduction pathways may be higher than those taken into consideration from canonical pathway representations. Scope of the present analysis is to provide a wider, systemic picture of the NF-κB signaling system. Data from different sources such as literature, functional enrichment web resources, protein-protein interaction and pathway databases have been gathered, curated, integrated and analyzed in order to reconstruct a single, comprehensive picture of the proteins that interact with, and participate to the NF-κB activation system. Such a reconstruction shows that the NF-κB interactome is substantially different in quantity and quality of components with respect to canonical representations. The analysis highlights that several neglected but topologically central proteins may play a role in the activation of NF-κB mediated responses. Moreover the interactome structure fits with the characteristics of a bow tie architecture. This interactome is intended as an open network resource available for further development, refinement and analysis.

Haploinsufficiency in the prometastasis Kiss1 receptor Gpr54 delays breast tumor initiation, progression, and lung metastasis

Activation of KISS1 receptor (KISS1R or GPR54) by its ligands (Kisspeptins) regulates a diverse function both in normal physiology and pathophysiology. In cancer, KISS1R has been implicated in tumor angiogenesis and metastasis, but a broader evaluation of KISS1R in tumorigenesis and tumor progression is yet to be conducted. In this study, we used mouse models of Kiss1r gene knockout and mouse mammary tumor virus-polyoma virus middle T antigen (MMTV-PyMT)-induced breast cancer to conduct such an evaluation. Kiss1r heterozygosity in MMTV-PyMT mice was sufficient to attenuate breast cancer initiation, growth, latency, multiplicity, and lung metastasis. To confirm these effects and assess possible contributions of endogenous ligands, we isolated primary tumor cells from PyMT/Kiss1r(+/+) and PyMT/Kiss1r(+/-) mice and compared their phenotypes by in vitro and in vivo assays. Kiss1r loss attenuated in vitro tumorigenic properties as well as tumor growth in vivo in immunocompromised NOD.SCID/NCr mice. Kiss1r activation in these cells, resulting from the addition of its ligand Kisspeptin-10, resulted in RhoA activation and RhoA-dependent gene expression through the Gαq-p63RhoGEF signaling pathway. Anchorage-independent growth was tightly linked to dose-dependent regulation of RhoA by Kiss1r. In support of these results, siRNA-mediated knockdown of KISS1R or inactivation of RhoA in human MCF10A breast epithelial cells overexpressing H-RasV12 was sufficient to reduce Ras-induced anchorage-independent growth. In summary, we concluded that Kiss1r attenuation was sufficient to delay breast tumor initiation, progression, and metastasis through inhibitory effects on the downstream Gαq-p63RhoGEF-RhoA signaling pathway.

Towards genome-scale signalling network reconstructions

Biological signalling networks allow living organisms to issue an integrated response to current conditions and make limited predictions about future environmental changes. Small-scale dynamic models of signalling cascades, including mitogen-activated protein kinase cascades, have been developed to generate hypotheses about signal transduction. Owing to technical limitations, these models and the hypotheses they generate have focused on a limited subset of signalling molecules. Now that we can simultaneously measure a substantial portion of the molecular components of a cell, we can begin to develop and test systems-level models of cellular signalling and regulatory processes, therefore gaining insights into the 'thought' processes of a cell.

Automated ensemble modeling with modelMaGe: analyzing feedback mechanisms in the Sho1 branch of the HOG pathway

In systems biology uncertainty about biological processes translates into alternative mathematical model candidates. Here, the goal is to generate, fit and discriminate several candidate models that represent different hypotheses for feedback mechanisms responsible for downregulating the response of the Sho1 branch of the yeast high osmolarity glycerol (HOG) signaling pathway after initial stimulation. Implementing and testing these candidate models by hand is a tedious and error-prone task. Therefore, we automatically generated a set of candidate models of the Sho1 branch with the tool modelMaGe. These candidate models are automatically documented, can readily be simulated and fitted automatically to data. A ranking of the models with respect to parsimonious data representation is provided, enabling discrimination between candidate models and the biological hypotheses underlying them. We conclude that a previously published model fitted spurious effects in the data. Moreover, the discrimination analysis suggests that the reported data does not support the conclusion that a desensitization mechanism leads to the rapid attenuation of Hog1 signaling in the Sho1 branch of the HOG pathway. The data rather supports a model where an integrator feedback shuts down the pathway. This conclusion is also supported by dedicated experiments that can exclusively be predicted by those models including an integrator feedback.

modelMaGe is an open source project and is distributed under the Gnu General Public License (GPL) and is available from http://modelmage.org.

Linking the proteins--elucidation of proteome-scale networks using mass spectrometry

Proteomes are intricate. Typically, thousands of proteins interact through physical association and post-translational modifications (PTMs) to give rise to the emergent functions of cells. Understanding these functions requires one to study proteomes as "systems" rather than collections of individual protein molecules. The abstraction of the interacting proteome to "protein networks" has recently gained much attention, as networks are effective representations, that lose specific molecular details, but provide the ability to see the proteome as a whole. Mostly two aspects of the proteome have been represented by network models: proteome-wide physical protein-protein-binding interactions organized into Protein Interaction Networks (PINs), and proteome-wide PTM relations organized into Protein Signaling Networks (PSNs). Mass spectrometry (MS) techniques have been shown to be essential to reveal both of these aspects on a proteome-wide scale. Techniques such as affinity purification followed by MS have been used to elucidate protein-protein interactions, and MS-based quantitative phosphoproteomics is critical to understand the structure and dynamics of signaling through the proteome. We here review the current state-of-the-art MS-based analytical pipelines for the purpose to characterize proteome-scale networks.

Integrating Omics data for signaling pathways, interactome reconstruction, and functional analysis

Omics data and computational approaches are today providing a key to disentangle the complex architecture of living systems. The integration and analysis of data of different nature allows to extract meaningful representations of signaling pathways and protein interactions networks, helpful in achieving an increased understanding of such intricate biochemical processes. We here describe a general workflow and relative hurdles in integrating online Omics data and analyzing reconstructed representations by using the available computational platforms.

Identification of optimal drug combinations targeting cellular networks: integrating phospho-proteomics and computational network analysis

Targeted therapeutics hold tremendous promise in inhibiting cancer cell proliferation. However, targeting proteins individually can be compensated for by bypass mechanisms and activation of regulatory loops. Designing optimal therapeutic combinations must therefore take into consideration the complex dynamic networks in the cell. In this study, we analyzed the insulin-like growth factor (IGF-1) signaling network in the MDA-MB231 breast cancer cell line. We used reverse-phase protein array to measure the transient changes in the phosphorylation of proteins after IGF-1 stimulation. We developed a computational procedure that integrated mass action modeling with particle swarm optimization to train the model against the experimental data and infer the unknown model parameters. The trained model was used to predict how targeting individual signaling proteins altered the rest of the network and identify drug combinations that minimally increased phosphorylation of other proteins elsewhere in the network. Experimental testing of the modeling predictions showed that optimal drug combinations inhibited cell signaling and proliferation, whereas nonoptimal combination of inhibitors increased phosphorylation of nontargeted proteins and rescued cells from cell death. The integrative approach described here is useful for generating experimental intervention strategies that could optimize drug combinations and discover novel pharmacologic targets for cancer therapy.

From 'differential expression' to 'differential networking' - identification of dysfunctional regulatory networks in diseases

Understanding diseases requires identifying the differences between healthy and affected tissues. Gene expression data have revolutionized the study of diseases by making it possible to simultaneously consider thousands of genes. The identification of disease-associated genes requires studying the genes in the context of the regulatory systems they are involved in. A major goal is to identify specific regulatory networks that are dysfunctional in a given disease state. Although we still have not reached a stage where the elucidation of differential regulatory networks is commonly feasible, recent advances have described the first steps towards this goal - the identification of differential coexpression networks. This review describes the shift from differential gene expression to differential networking and outlines how this shift will affect the study of the genetic basis of disease.

Elucidation of functional consequences of signalling pathway interactions

BACKGROUND

A great deal of data has accumulated on signalling pathways. These large datasets are thought to contain much implicit information on their molecular structure, interaction and activity information, which provides a picture of intricate molecular networks believed to underlie biological functions. While tremendous advances have been made in trying to understand these systems, how information is transmitted within them is still poorly understood. This ever growing amount of data demands we adopt powerful computational techniques that will play a pivotal role in the conversion of mined data to knowledge, and in elucidating the topological and functional properties of protein - protein interactions.

RESULTS

A computational framework is presented which allows for the description of embedded networks, and identification of common shared components thought to assist in the transmission of information within the systems studied. By employing the graph theories of network biology - such as degree distribution, clustering coefficient, vertex betweenness and shortest path measures - topological features of protein-protein interactions for published datasets of the p53, nuclear factor kappa B (NF-kappaB) and G1/S phase of the cell cycle systems were ascertained. Highly ranked nodes which in some cases were identified as connecting proteins most likely responsible for propagation of transduction signals across the networks were determined. The functional consequences of these nodes in the context of their network environment were also determined. These findings highlight the usefulness of the framework in identifying possible combination or links as targets for therapeutic responses; and put forward the idea of using retrieved knowledge on the shared components in constructing better organised and structured models of signalling networks.

CONCLUSION

It is hoped that through the data mined reconstructed signal transduction networks, well developed models of the published data can be built which in the end would guide the prediction of new targets based on the pathway's environment for further analysis. Source code is available upon request.

Signaling logic of activity-triggered dendritic protein synthesis: an mTOR gate but not a feedback switch

Changes in synaptic efficacy are believed to form the cellular basis for memory. Protein synthesis in dendrites is needed to consolidate long-term synaptic changes. Many signals converge to regulate dendritic protein synthesis, including synaptic and cellular activity, and growth factors. The coordination of these multiple inputs is especially intriguing because the synthetic and control pathways themselves are among the synthesized proteins. We have modeled this system to study its molecular logic and to understand how runaway feedback is avoided. We show that growth factors such as brain-derived neurotrophic factor (BDNF) gate activity-triggered protein synthesis via mammalian target of rapamycin (mTOR). We also show that bistability is unlikely to arise from the major protein synthesis pathways in our model, even though these include several positive feedback loops. We propose that these gating and stability properties may serve to suppress runaway activation of the pathway, while preserving the key role of responsiveness to multiple sources of input.

Memory formation involves the controlled production of new proteins close to the site of input stimuli on nerve cells. Strong inputs, in combination with growth factors, stimulate the synthesis of several kinds of synaptic proteins. These new proteins are believed to participate in remodeling the contacts between cells. This gives rise to a potentially unstable situation of a self-modifying cellular machine, because the new proteins rebuild their own inputs and their own production machinery. We have analyzed these interactions by modeling multiple inputs and the process of self-modifying feedback. We find that runaway modifications are prevented in two ways: first, a molecule called mTOR acts as a gate to suppress synthesis except under very tightly regulated conditions. Second, the feedback processes operate in a range where it is very unlikely that they can give rise to runaway buildup. Thus, the system avoids instability even though it is capable of modifying itself in response to many kinds of inputs.

Computing algebraic functions with biochemical reaction networks

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Neurotrophic factors switch between two signaling pathways that trigger axonal growth

Integration of multiple inputs from the extracellular environment, such as extracellular matrix molecules and growth factors, is a crucial process for cell function and information processing in multicellular organisms. Here we demonstrate that co-stimulation of dorsal root ganglion neurons with neurotrophic factors (NTFs) – glial-cell-line-derived neurotrophic factor, neurturin or nerve growth factor – and laminin leads to axonal growth that requires activation of Src family kinases (SFKs). A different, SFK-independent signaling pathway evokes axonal growth on laminin in the absence of the NTFs. By contrast, axonal branching is regulated by SFKs both in the presence and in the absence of NGF. We propose and experimentally verify a Boolean model of the signaling network triggered by NTFs and laminin. Our results demonstrate that NTFs provide an environmental cue that triggers a switch between separate pathways in the cell signaling network.

Bridging the gap between in silico and cell-based analysis of the nuclear factor-kappaB signaling pathway by in vitro studies of IKK2

Previously, we have shown by sensitivity analysis, that the oscillatory behavior of nuclear factor (NF-kappaB) is coupled to free IkappaB kinase-2 (IKK2) and IkappaBalpha(IkappaBalpha), and that the phosphorylation of IkappaBalpha by IKK influences the amplitude of NF-kappaB oscillations. We have performed further analyses of the behavior of NF-kappaB and its signal transduction network to understand the dynamics of this system. A time lapse study of NF-kappaB translocation in 10,000 cells showed discernible oscillations in levels of nuclear NF-kappaB amongst cells when stimulated with interleukin (IL-1alpha), which suggests a small degree of synchronization amongst the cell population. When the kinetics for the phosphorylation of IkappaBalpha by IKK were measured, we found that the values for the affinity and catalytic efficiency of IKK2 for IkappaBalpha were dependent on assay conditions. The application of these kinetic parameters in our computational model of the NF-kappaB pathway resulted in significant differences in the oscillatory patterns of NF-kappaB depending on the rate constant value used. Hence, interpretation of in silico models should be made in the context of this uncertainty.

Computational realizations of living systems

Robert Rosen's central theorem states that organisms are fundamentally different from machines, mainly because they are "closed with respect to effcient causation." The proof for this theorem rests on two crucial assumptions. The first is that for a certain class of systems ("mechanisms") analytic modeling is the inverse of synthetic modeling. The second is that aspects of machines can be modeled using relational models and that these relational models are themselves refined by at least one analytic model. We show that both assumptions are unjustified. We conclude that these results cast serious doubts on the validity of Rosen's proof.

Parameter estimate of signal transduction pathways

BACKGROUND

The "inverse" problem is related to the determination of unknown causes on the bases of the observation of their effects. This is the opposite of the corresponding "direct" problem, which relates to the prediction of the effects generated by a complete description of some agencies. The solution of an inverse problem entails the construction of a mathematical model and takes the moves from a number of experimental data. In this respect, inverse problems are often ill-conditioned as the amount of experimental conditions available are often insufficient to unambiguously solve the mathematical model. Several approaches to solving inverse problems are possible, both computational and experimental, some of which are mentioned in this article. In this work, we will describe in details the attempt to solve an inverse problem which arose in the study of an intracellular signaling pathway.

RESULTS

Using the Genetic Algorithm to find the sub-optimal solution to the optimization problem, we have estimated a set of unknown parameters describing a kinetic model of a signaling pathway in the neuronal cell. The model is composed of mass action ordinary differential equations, where the kinetic parameters describe protein-protein interactions, protein synthesis and degradation. The algorithm has been implemented on a parallel platform. Several potential solutions of the problem have been computed, each solution being a set of model parameters. A sub-set of parameters has been selected on the basis on their small coefficient of variation across the ensemble of solutions.

CONCLUSION

Despite the lack of sufficiently reliable and homogeneous experimental data, the genetic algorithm approach has allowed to estimate the approximate value of a number of model parameters in a kinetic model of a signaling pathway: these parameters have been assessed to be relevant for the reproduction of the available experimental data.

Theodor Bücher Lecture. Metabolomics, modelling and machine learning in systems biology - towards an understanding of the languages of cells. Delivered on 3 July 2005 at the 30th FEBS Congress and the 9th IUBMB conference in Budapest

The newly emerging field of systems biology involves a judicious interplay between high-throughput 'wet' experimentation, computational modelling and technology development, coupled to the world of ideas and theory. This interplay involves iterative cycles, such that systems biology is not at all confined to hypothesis-dependent studies, with intelligent, principled, hypothesis-generating studies being of high importance and consequently very far from aimless fishing expeditions. I seek to illustrate each of these facets. Novel technology development in metabolomics can increase substantially the dynamic range and number of metabolites that one can detect, and these can be exploited as disease markers and in the consequent and principled generation of hypotheses that are consistent with the data and achieve this in a value-free manner. Much of classical biochemistry and signalling pathway analysis has concentrated on the analyses of changes in the concentrations of intermediates, with 'local' equations - such as that of Michaelis and Menten v=(Vmax x S)/(S+K m) - that describe individual steps being based solely on the instantaneous values of these concentrations. Recent work using single cells (that are not subject to the intellectually unsupportable averaging of the variable displayed by heterogeneous cells possessing nonlinear kinetics) has led to the recognition that some protein signalling pathways may encode their signals not (just) as concentrations (AM or amplitude-modulated in a radio analogy) but via changes in the dynamics of those concentrations (the signals are FM or frequency-modulated). This contributes in principle to a straightforward solution of the crosstalk problem, leads to a profound reassessment of how to understand the downstream effects of dynamic changes in the concentrations of elements in these pathways, and stresses the role of signal processing (and not merely the intermediates) in biological signalling. It is this signal processing that lies at the heart of understanding the languages of cells. The resolution of many of the modern and postgenomic problems of biochemistry requires the development of a myriad of new technologies (and maybe a new culture), and thus regular input from the physical sciences, engineering, mathematics and computer science. One solution, that we are adopting in the Manchester Interdisciplinary Biocentre (http://www.mib.ac.uk/) and the Manchester Centre for Integrative Systems Biology (http://www.mcisb.org/), is thus to colocate individuals with the necessary combinations of skills. Novel disciplines that require such an integrative approach continue to emerge. These include fields such as chemical genomics, synthetic biology, distributed computational environments for biological data and modelling, single cell diagnostics/bionanotechnology, and computational linguistics/text mining.

Synergistic control of oscillations in the NF-B signalling pathway

In previous work, we studied the behaviour of a model of part of the NF-kappaB signalling pathway. The model displayed oscillations that varied both in number, amplitude and frequency when its parameters were varied. Sensitivity analysis showed that just nine of the 64 reaction parameters were mainly responsible for the control of the oscillations when these parameters were varied individually. However, the control of the properties of any complex system is distributed, and, as many of these reactions are highly non-linear, we expect that their interactions will be too. Pairwise modulation of these nine parameters gives a search space some 50 times smaller (81 against 4096) than that required for the pairwise modulation of all 64 reactions, and this permitted their study (which would otherwise have been effectively intractable). Strikingly synergistic effects were observed, in which the effect of one of the parameters was strongly (and even qualitatively) dependent on the values of another parameter. Regions of parameter space could be found in which the amplitude, but not the frequency (timing), of oscillations varied, and vice versa. Such modelling will permit the design and performance of experiments aimed at disentangling the role of the dynamics of oscillations, rather than simply their amplitude, in determining cell fate. Overall, the analyses reveal a level of complexity in these dynamic models that is not apparent from study of their individual parameters alone and point to the value of manipulating multiple elements of complex networks to achieve desired physiological effects.

Quantitative analysis of signaling networks

The response of biological cells to environmental change is coordinated by protein-based signaling networks. These networks are to be found in both prokaryotes and eukaryotes. In eukaryotes, the signaling networks can be highly complex, some networks comprising of 60 or more proteins. The fundamental motif that has been found in all signaling networks is the protein phosphorylation/dephosphorylation cycle--the cascade cycle. At this time, the computational function of many of the signaling networks is poorly understood. However, it is clear that it is possible to construct a huge variety of control and computational circuits, both analog and digital from combinations of the cascade cycle. In this review, we will summarize the great versatility of the simple cascade cycle as a computational unit and towards the end give two examples, one prokaryotic chemotaxis circuit and the other, the eukaryotic MAPK cascade.

Computational physiology and the Physiome Project

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization--from proteins to cells, tissues, organs and organ systems--these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.

A more efficient search strategy for aging genes based on connectivity

MOTIVATION

Many aging genes have been found from unbiased screens in model organisms. Genetic interventions promoting longevity are usually quantitative, while in many other biological fields (e.g. development) null mutations alone have been very informative. Therefore, in the case of aging the task is larger and the need for a more efficient genetic search strategy is especially strong.

RESULTS

The topology of genetic and metabolic networks is organized according to a scale-free distribution, in which hubs with large numbers of links are present. We have developed a computational model of aging genes as the hubs of biological networks. The computational model shows that, after generalized damage, the function of a network with scale-free topology can be significantly restored by a limited intervention on the hubs. Analyses of data on aging genes and biological networks support the applicability of the model to biological aging. The model also might explain several of the properties of aging genes, including the high degree of conservation across different species. The model suggests that aging genes tend to have a higher number of connections and therefore supports a strategy, based on connectivity, for prioritizing what might otherwise be a random search for aging genes.

Genomics view of gonadotrope signaling circuits

Gonadotropin-releasing hormone (GnRH) binds to the pituitary GnRH receptor to activate signal transduction cascades that ultimately modulate gonadotropin biosynthesis. Comprehensive studies of the GnRH-activated gene program in the LbetaT2 gonadotrope cell line have greatly increased our knowledge of the number of early and intermediate gene transcripts that are modulated by GnRH. Among the classes of gene induced are several whose protein products provide feedback to various levels of signaling pathways, suggesting that gene induction forms an integral component of signal transduction and contributes to longer-timescale feedback and feedforward loops. High-throughput quantitative genomic studies, mathematical modeling and biochemical studies are beginning to delineate the organization and function of the signal-decoding and logic circuit modules of the gonadotrope's signal transduction network.

Current status and challenges in connecting models of erythrocyte metabolism to experimental reality

Detailed kinetic models of human erythrocyte metabolism have served to summarize the vast literature and to predict outcomes from laboratory and "Nature's" experiments on this simple cell. Mathematical methods for handling the large array of nonlinear ordinary differential equations that describe the time dependence of this system are well developed, but experimental methods that can guide the evolution of the models are in short supply. NMR spectroscopy is one method that is non-selective with respect to analyte detection but is highly specific with respect to their identification and quantification. Thus time courses of metabolism are readily recorded for easily changed experimental conditions. While the data can be simulated, the systems of equations are too complex to allow solutions of the inverse problem, namely parameter-value estimation for the large number of enzyme and membrane-transport reactions operating in situ as opposed to in vitro. Other complications with the modelling include the dependence of cell volume on time, and the rates of membrane transport processes are often dependent on the membrane potential. These matters are discussed in the light of new modelling strategies.

Improved methods for the mathematically controlled comparison of biochemical systems

The method of mathematically controlled comparison provides a structured approach for the comparison of alternative biochemical pathways with respect to selected functional effectiveness measures. Under this approach, alternative implementations of a biochemical pathway are modeled mathematically, forced to be equivalent through the application of selected constraints, and compared with respect to selected functional effectiveness measures. While the method has been applied successfully in a variety of studies, we offer recommendations for improvements to the method that (1) relax requirements for definition of constraints sufficient to remove all degrees of freedom in forming the equivalent alternative, (2) facilitate generalization of the results thus avoiding the need to condition those findings on the selected constraints, and (3) provide additional insights into the effect of selected constraints on the functional effectiveness measures. We present improvements to the method and related statistical models, apply the method to a previously conducted comparison of network regulation in the immune system, and compare our results to those previously reported.

Regulation of neuromodulator receptor efficacy—implications for whole-neuron and synaptic plasticity

Membrane receptors for neuromodulators (NM) are highly regulated in their distribution and efficacy-a phenomenon which influences the individual cell's response to central signals of NM release. Even though NM receptor regulation is implicated in the pharmacological action of many drugs, and is also known to be influenced by various environmental factors, its functional consequences and modes of action are not well understood. In this paper we summarize relevant experimental evidence on NM receptor regulation (specifically dopamine D1 and D2 receptors) in order to explore its significance for neural and synaptic plasticity. We identify the relevant components of NM receptor regulation (receptor phosphorylation, receptor trafficking and sensitization of second-messenger pathways) gained from studies on cultured cells. Key principles in the regulation and control of short-term plasticity (sensitization) are identified, and a model is presented which employs direct and indirect feedback regulation of receptor efficacy. We also discuss long-term plasticity which involves shifts in receptor sensitivity and loss of responsivity to NM signals. Finally, we discuss the implications of NM receptor regulation for models of brain plasticity and memorization. We emphasize that a realistic model of brain plasticity will have to go beyond Hebbian models of long-term potentiation and depression. Plasticity in the distribution and efficacy of NM receptors may provide another important source of functional plasticity with implications for learning and memory.

Dynamical and integrative cell signaling: challenges for the new biology

Years of careful experimental analysis have revealed that signaling molecules are organized into complex networks of biochemical reactions exquisitely regulated in time and space to provide a cell with high-fidelity information about an extremely noisy and volatile environment. A new view of signaling networks as systems consisting of multiple complex elements interacting in a multifarious fashion is emerging, a view that conflicts with the single-gene or protein-centric approach common in biological research. The postgenomic era has brought about a different, network-centric methodology of analysis, suddenly forcing researchers toward the opposite extreme of complexity, where the networks being explored are, to a certain extent, intractable and uninterpretable. Both the cartoons of simple pathways and the very large "hair-ball" diagrams of large intracellular networks are also representations of static worlds, superficially devoid of dynamics and chemistry. These representations are often viewed as being analogous to stably linked computer and neural networks rather than dynamically changing networks of chemical interactions, where the notions of concentration, compartmentalization, and diffusion may be the primary determinants of connectivity. Arguably, the systems biology approach, relying on computational modeling coupled with various experimental techniques and methodologies, will be an essential component of analysis of the behavior of signal transduction pathways. Combining the dynamical view of rapidly evolving responses and the structural view arising from high-throughput analyses of the interacting species will be the best approach toward efforts toward greater understanding of intracellular signaling processes.