Quantitative analysis of signaling networks

Single-cell morphodynamical trajectories enable prediction of gene expression accompanying cell state change

Extracellular signals induce changes to molecular programs that modulate multiple cellular phenotypes, including proliferation, motility, and differentiation status. The connection between dynamically adapting phenotypic states and the molecular programs that define them is not well understood. Here we develop data-driven models of single-cell phenotypic responses to extracellular stimuli by linking gene transcription levels to "morphodynamics" - changes in cell morphology and motility observable in time-lapse image data. We adopt a dynamics-first view of cell state by grouping single-cell trajectories into states with shared morphodynamic responses. The single-cell trajectories enable development of a first-of-its-kind computational approach to map live-cell dynamics to snapshot gene transcript levels, which we term MMIST, Molecular and Morphodynamics-Integrated Single-cell Trajectories. The key conceptual advance of MMIST is that cell behavior can be quantified based on dynamically defined states and that extracellular signals alter the overall distribution of cell states by altering rates of switching between states. We find a cell state landscape that is bound by epithelial and mesenchymal endpoints, with distinct sequences of epithelial to mesenchymal transition (EMT) and mesenchymal to epithelial transition (MET) intermediates. The analysis yields predictions for gene expression changes consistent with curated EMT gene sets and provides a prediction of thousands of RNA transcripts through extracellular signal-induced EMT and MET with near-continuous time resolution. The MMIST framework leverages true single-cell dynamical behavior to generate molecular-level omics inferences and is broadly applicable to other biological domains, time-lapse imaging approaches and molecular snapshot data.

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.

First-order ultrasensitivity in phosphorylation cycles

Cellular signal transduction takes place through a network of phosphorylation cycles. These pathways take the form of a multi-layered cascade of cycles. This work focuses on the sensitivity of single, double and n length cycles. Cycles that operate in the zero-order regime can become sensitive to changes in signal, resulting in zero-order ultrasensitivity (ZOU). Using frequency analysis, we confirm previous efforts that cascades can act as noise filters by computing the bandwidth. We show that n length cycles display what we term first-order ultrasensitivity which occurs even when the cycles are not operating in the zero-order regime. The magnitude of the sensitivity, however, has an upper bound equal to the number of cycles. It is known that ZOU can be significantly reduced in the presence of retroactivity. We show that the first-order ultrasensitivity is immune to retroactivity and that the ZOU and first-order ultrasensitivity can be blended to create systems with constant sensitivity over a wider range of signal. We show that the ZOU in a double cycle is only modestly higher compared with a single cycle. We therefore speculate that the double cycle has evolved to enable amplification even in the face of retroactivity.

Sensitivity and Frequency Response of Biochemical Cascades

Signal transduction from a cell's surface to cytoplasmic and nuclear targets takes place through a complex network of interconnected pathways. Phosphorylation cycles are common components of many pathways and may take the form of a multi-layered cascade of cycles or incorporate species with multiple phosphorylation sites that effectively create a sequence of cycles with increasing states of phosphorylation. This work focuses on the frequency response and sensitivity of such systems, two properties that have not been thoroughly examined. Starting with a singularly phosphorylated single-cycle system, we compare the sensitivity to perturbation at steady-state across a range of input signal strengths. This is followed by a frequency response analysis focusing on the gain and associated bandwidth. Next, we consider a two-layer cascade of single phosphorylation cycles and focus on how the two cycles interact to produce various effects on the bandwidth and damping properties. Then we consider the (ultra)sensitivity of a doubly phosphorylated system, where we describe in detail first-order ultrasensitivity, a unique property of these systems, which can be blended with zero-order ultrasensitivity to create systems with relatively constant gain over a range of signal input. Finally, we give an in-depth analysis of the sensitivity of an n-phosphorylated system.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

Gene by Environment Interactions reveal new regulatory aspects of signaling network plasticity

Phenotypes can change during exposure to different environments through the regulation of signaling pathways that operate in integrated networks. How signaling networks produce different phenotypes in different settings is not fully understood. Here, Gene by Environment Interactions (GEIs) were used to explore the regulatory network that controls filamentous/invasive growth in the yeast Saccharomyces cerevisiae. GEI analysis revealed that the regulation of invasive growth is decentralized and varies extensively across environments. Different regulatory pathways were critical or dispensable depending on the environment, microenvironment, or time point tested, and the pathway that made the strongest contribution changed depending on the environment. Some regulators even showed conditional role reversals. Ranking pathways' roles across environments revealed an under-appreciated pathway (OPI1) as the single strongest regulator among the major pathways tested (RAS, RIM101, and MAPK). One mechanism that may explain the high degree of regulatory plasticity observed was conditional pathway interactions, such as conditional redundancy and conditional cross-pathway regulation. Another mechanism was that different pathways conditionally and differentially regulated gene expression, such as target genes that control separate cell adhesion mechanisms (FLO11 and SFG1). An exception to decentralized regulation of invasive growth was that morphogenetic changes (cell elongation and budding pattern) were primarily regulated by one pathway (MAPK). GEI analysis also uncovered a round-cell invasion phenotype. Our work suggests that GEI analysis is a simple and powerful approach to define the regulatory basis of complex phenotypes and may be applicable to many systems.

Robust adaptation of PKCζ-IRS1 insulin signaling pathways through integral feedback control

Insulin signaling pathways in muscle tissue play a major role in maintaining glucose homeostasis. Dysregulation in these pathways results in the onset of serious metabolic disorders like type 2 diabetes. Robustness is an essential characteristic of insulin signaling pathways that ensures reliable signal transduction in the presence of perturbations as a result of several feedback mechanisms. Integral control, according to control engineering, provides reliable setpoint tracking and disturbance rejection. The presence of negative feedback and integrating process is crucial for biological processes to achieve integral control. The existence of an integral controller leads to the rejection of perturbations which resulted in the robust regulation of biochemical entities within acceptable levels. In the presentin silicoresearch work, the presence of integral control in the protein kinase Cζ- insulin receptor substrate-1 (PKCζ-IRS1) pathway is identified, verified mathematically and model is simulated in Cell Designer. The data is exported to Minitab software and robustness analysis is carried out statistically using the Mann-Whitney test. The p-value of the results obtained with given parameters perturbed by ±1% is greater than the significance level of 0.05 (0.2132 for 1% error in k7(rate constant of IRS1 phosphorylation), 0.2096 for -1% error in k7, 0.9037 for both ±1% error in insulin and 0.9037 for ±1% error in k1(association rate constant of the first molecule of insulin to bind the insulin receptor), indicated that our hypothesis is proved The results satisfactorily indicate that even when perturbations are present, glucose homeostasis in muscle tissue is robust due to the presence of integral regulation in the PKCζ-IRS1 insulin signaling pathways. In this paper, we have analysed the findings from the framework of robust control theory, which has allowed us to examine that how PKCζ-IRS1 insulin signaling pathways produces desired output in presence of perturbations.

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

Advanced Chemical Computing Using Discrete Turing Patterns in Arrays of Coupled Cells

We examine dynamical switching among discrete Turing patterns that enable chemical computing performed by mass-coupled reaction cells arranged as arrays with various topological configurations: three coupled cells in a cyclic array, four coupled cells in a linear array, four coupled cells in a cyclic array, and four coupled cells in a branched array. Each cell is operating as a continuous stirred tank reactor, within which the glycolytic reaction takes place, represented by a skeleton inhibitor-activator model where ADP plays the role of activator and ATP is the inhibitor. The mass coupling between cells is assumed to be operating in three possible transport regimes: (i) equal transport coefficients of the inhibitor and activator (ii) slightly faster transport of the activator, and (iii) strongly faster transport of the inhibitor. Each cellular array is characterized by two pairs of tunable parameters, the rate coefficients of the autocatalytic and inhibitory steps, and the transport coefficients of the coupling. Using stability and bifurcation analysis we identified conditions for occurrence of discrete Turing patterns associated with non-uniform stationary states. We found stable symmetric and/or asymmetric discrete Turing patterns coexisting with stable uniform periodic oscillations. To switch from one of the coexisting stable regimes to another we use carefully targeted perturbations, which allows us to build systems of logic gates specific to each topological type of the array, which in turn enables to perform advanced modes of chemical computing. By combining chemical computing techniques in the arrays with glycolytic excitable channels, we propose a cellular assemblage design for advanced chemical computing.

The quasi-steady-state approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics

In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their respective critical manifolds. By combining Tikhonov-Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation error for the standard, reverse and total quasi-steady-state approximations. Furthermore, previous analyses suggest that the reverse quasi-steady-state approximation is only valid when initial enzyme concentrations greatly exceed initial substrate concentrations. However, our results indicate that this approximation can be valid when initial enzyme and substrate concentrations are of equal magnitude. Using energy methods, we find that the condition for the validity of the reverse quasi-steady-state approximation is far less restrictive than was previously assumed, and we derive a new "small" parameter that determines the validity of this approximation. In doing so, we extend the established domain of validity for the reverse quasi-steady-state approximation. Consequently, this opens up the possibility of utilizing the reverse quasi-steady-state approximation to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought. Moreover, we show for the first time that the critical manifold of the reverse quasi-steady-state approximation contains a singular point where normal hyperbolicity is lost. Associated with this singularity is a transcritical bifurcation, and the corresponding normal form of this bifurcation is recovered through scaling analysis.

Bifurcation analysis of insulin regulated mTOR signalling pathway in cancer cells

Insulin induced mTOR signalling pathway is a complex network implicated in many types of cancers. The molecular mechanism of this pathway is highly complex and the dynamics is tightly regulated by intricate positive and negative feedback loops. In breast cancer cell lines, metformin has been shown to induce phosphorylation at specific serine sites in insulin regulated substrate of mTOR pathway that results in apoptosis over cell proliferation. The author models and performs bifurcation analysis to simulate cell proliferation and apoptosis in mTOR signalling pathway to capture the dynamics both in the presence and absence of metformin in cancer cells. Metformin is shown to negatively regulate PI3K through AMPK induced IRS1 phosphorylation and this brings about a reversal of AKT bistablity in codimension-1 bifurcation diagram from S-shaped, related to cell proliferation in the absence of drug metformin, to Z-shaped, related to apoptosis in the presence of drug metformin. The author hypothesises and explains how this negative regulation acts a circuit breaker, as a result of which mTOR network favours apoptosis of cancer cells over its proliferation. The implication of reversing the shape of bistable dynamics from S to Z or vice-versa in biological networks in general is discussed.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Signaling Architectures that Transmit Unidirectional Information Despite Retroactivity

A signaling pathway transmits information from an upstream system to downstream systems, ideally in a unidirectional fashion. A key obstacle to unidirectional transmission is retroactivity, the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the fundamental question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general procedure based on mathematical analysis that provides an answer to this question. Using this procedure, we analyze the ability of a variety of signaling architectures to transmit one-way (from upstream to downstream) signals, as key biological parameters are tuned. We find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show a stringent design tradeoff that hampers their ability to overcome retroactivity. Interestingly, cascades of these architectures, which are highly represented in nature, can overcome this tradeoff and thus enable unidirectional transmission. By contrast, phosphotransfer systems, and single and double phosphorylation cycles that transmit signals from a substrate, are unable to mitigate retroactivity effects, even when cascaded, and hence are not well suited for unidirectional information transmission. These results are largely independent of the specific reaction-rate constant values, and depend on the topology of the architectures. Our results therefore identify signaling architectures that, allowing unidirectional transmission of signals, embody modular processes that conserve their input/output behavior across multiple contexts. These findings can be used to decompose natural signal transduction networks into modules, and at the same time, they establish a library of devices that can be used in synthetic biology to facilitate modular circuit design.

Synthetic Biology: Engineering Living Systems from Biophysical Principles

Synthetic biology was founded as a biophysical discipline that sought explanations for the origins of life from chemical and physical first principles. Modern synthetic biology has been reinvented as an engineering discipline to design new organisms as well as to better understand fundamental biological mechanisms. However, success is still largely limited to the laboratory and transformative applications of synthetic biology are still in their infancy. Here, we review six principles of living systems and how they compare and contrast with engineered systems. We cite specific examples from the synthetic biology literature that illustrate these principles and speculate on their implications for further study. To fully realize the promise of synthetic biology, we must be aware of life's unique properties.

Push-Pull and Feedback Mechanisms Can Align Signaling System Outputs with Inputs

Many cell signaling systems, including the yeast pheromone response system, exhibit "dose-response alignment" (DoRA), in which output of one or more downstream steps closely matches the fraction of occupied receptors. DoRA can improve the fidelity of transmitted dose information. Here, we searched systematically for biochemical network topologies that produced DoRA. Most networks, including many containing feedback and feedforward loops, could not produce DoRA. However, networks including "push-pull" mechanisms, in which the active form of a signaling species stimulates downstream activity and the nominally inactive form reduces downstream activity, enabled perfect DoRA. Networks containing feedbacks enabled DoRA, but only if they also compared feedback to input and adjusted output to match. Our results establish push-pull as a non-feedback mechanism to align output with variable input and maximize information transfer in signaling systems. They also suggest genetic approaches to determine whether particular signaling systems use feedback or push-pull control.

How time delay and network design shape response patterns in biochemical negative feedback systems

BACKGROUND

Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks.

RESULTS

We investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not.

CONCLUSIONS

Our theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.

The role of time delay in adaptive cellular negative feedback systems

Adaptation in cellular systems is often mediated by negative feedbacks, which usually come with certain time delays causing several characteristic response patterns including an overdamped response, damped or sustained oscillations. Here, we analyse generic two-dimensional delay differential equations with delayed negative feedback describing the dynamics of biochemical adaptive signal-response networks. We derive explicit thresholds and boundaries showing how time delay determines characteristic response patterns of these networks. Applying our theoretical analyses to concrete data we show that adaptation to osmotic stress in yeast is optimal in the sense of minimizing adaptation time without causing oscillatory behaviour, i.e., a critically damped response. In addition, our framework demonstrates that a slight increase of time delay in the NF-κB system might induce a switch from damped to sustained oscillatory behaviour. Thus, we demonstrate how delay differential equations can be used to explicitly study the delay in biochemical negative feedback systems. Our analysis also provides insight into how time delay may tune biological signal-response patterns and control the systems behaviour.

Pancreatic Beta Cell G-Protein Coupled Receptors and Second Messenger Interactions: A Systems Biology Computational Analysis

Insulin secretory in pancreatic beta-cells responses to nutrient stimuli and hormonal modulators include multiple messengers and signaling pathways with complex interdependencies. Here we present a computational model that incorporates recent data on glucose metabolism, plasma membrane potential, G-protein-coupled-receptors (GPCR), cytoplasmic and endoplasmic reticulum calcium dynamics, cAMP and phospholipase C pathways that regulate interactions between second messengers in pancreatic beta-cells. The values of key model parameters were inferred from published experimental data. The model gives a reasonable fit to important aspects of experimentally measured metabolic and second messenger concentrations and provides a framework for analyzing the role of metabolic, hormones and neurotransmitters changes on insulin secretion. Our analysis of the dynamic data provides support for the hypothesis that activation of Ca²⁺-dependent adenylyl cyclases play a critical role in modulating the effects of glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP) and catecholamines. The regulatory properties of adenylyl cyclase isoforms determine fluctuations in cytoplasmic cAMP concentration and reveal a synergistic action of glucose, GLP-1 and GIP on insulin secretion. On the other hand, the regulatory properties of phospholipase C isoforms determine the interaction of glucose, acetylcholine and free fatty acids (FFA) (that act through the FFA receptors) on insulin secretion. We found that a combination of GPCR agonists activating different messenger pathways can stimulate insulin secretion more effectively than a combination of GPCR agonists for a single pathway. This analysis also suggests that the activators of GLP-1, GIP and FFA receptors may have a relatively low risk of hypoglycemia in fasting conditions whereas an activator of muscarinic receptors can increase this risk. This computational analysis demonstrates that study of second messenger pathway interactions will improve understanding of critical regulatory sites, how different GPCRs interact and pharmacological targets for modulating insulin secretion in type 2 diabetes.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Frequency modulation of ERK activation dynamics rewires cell fate

Transient versus sustained ERK MAP kinase (MAPK) activation dynamics induce proliferation versus differentiation in response to epidermal (EGF) or nerve (NGF) growth factors in PC‐12 cells. Duration of ERK activation has therefore been proposed to specify cell fate decisions. Using a biosensor to measure ERK activation dynamics in single living cells reveals that sustained EGF/NGF application leads to a heterogeneous mix of transient and sustained ERK activation dynamics in distinct cells of the population, different than the population average. EGF biases toward transient, while NGF biases toward sustained ERK activation responses. In contrast, pulsed growth factor application can repeatedly and homogeneously trigger ERK activity transients across the cell population. These datasets enable mathematical modeling to reveal salient features inherent to the MAPK network. Ultimately, this predicts pulsed growth factor stimulation regimes that can bypass the typical feedback activation to rewire the system toward cell differentiation irrespective of growth factor identity.

The dynamic control of signal transduction networks in cancer cells

Cancer is often considered a genetic disease. However, much of the enormous plasticity of cancer cells to evolve different phenotypes, to adapt to challenging microenvironments and to withstand therapeutic assaults is encoded by the structure and spatiotemporal dynamics of signal transduction networks. In this Review, we discuss recent concepts concerning how the rich signalling dynamics afforded by these networks are regulated and how they impinge on cancer cell proliferation, survival, invasiveness and drug resistance. Understanding this dynamic circuitry by mathematical modelling could pave the way to new therapeutic approaches and personalized treatments.

Consequences of feedback in signal transduction for targeted therapies

Over the last two decades, many small-molecule inhibitors that target kinase signalling have been developed. More than 20 of these inhibitors are FDA (U.S. Food and Drug Administration)-approved and are now being used in the clinics to treat tumours; even more have entered clinical trials. However, resistance to these inhibitors, either intrinsic to the tumour or acquired during treatment, remains a major problem in targeted therapeutics. One of the mechanisms by which tumours become resistant is the rewiring of the signalling networks via feedback, by which the tumour cells re-activate signalling or activate alternative signalling pathways. In the present article, we review insights from recent quantitative signalling studies combining mathematical modelling and experiments that revealed how feedback rewires MAPK (mitogen-activated protein kinase)/PI3K (phosphoinositide 3-kinase) signalling upon treatment and how that affects drug sensitivity.

An integrated network visualization framework towards metabolic engineering applications

Background

Over the last years, several methods for the phenotype simulation of microorganisms, under specified genetic and environmental conditions have been proposed, in the context of Metabolic Engineering (ME). These methods provided insight on the functioning of microbial metabolism and played a key role in the design of genetic modifications that can lead to strains of industrial interest. On the other hand, in the context of Systems Biology research, biological network visualization has reinforced its role as a core tool in understanding biological processes. However, it has been scarcely used to foster ME related methods, in spite of the acknowledged potential.

Results

In this work, an open-source software that aims to fill the gap between ME and metabolic network visualization is proposed, in the form of a plugin to the OptFlux ME platform. The framework is based on an abstract layer, where the network is represented as a bipartite graph containing minimal information about the underlying entities and their desired relative placement. The framework provides input/output support for networks specified in standard formats, such as XGMML, SBGN or SBML, providing a connection to genome-scale metabolic models. An user-interface makes it possible to edit, manipulate and query nodes in the network, providing tools to visualize diverse effects, including visual filters and aspect changing (e.g. colors, shapes and sizes). These tools are particularly interesting for ME, since they allow overlaying phenotype simulation results or elementary flux modes over the networks.

Conclusions

The framework and its source code are freely available, together with documentation and other resources, being illustrated with well documented case studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0420-0) contains supplementary material, which is available to authorized users.

How to make a synthetic multicellular computer

Biological systems perform computations at multiple scales and they do so in a robust way. Engineering metaphors have often been used in order to provide a rationale for modeling cellular and molecular computing networks and as the basis for their synthetic design. However, a major constraint in this mapping between electronic and wet computational circuits is the wiring problem. Although wires are identical within electronic devices, they must be different when using synthetic biology designs. Moreover, in most cases the designed molecular systems cannot be reused for other functions. A new approximation allows us to simplify the problem by using synthetic cellular consortia where the output of the computation is distributed over multiple engineered cells. By evolving circuits in silico, we can obtain the minimal sets of Boolean units required to solve the given problem at the lowest cost using cellular consortia. Our analysis reveals that the basic set of logic units is typically non-standard. Among the most common units, the so called inverted IMPLIES (N-Implies) appears to be one of the most important elements along with the NOT and AND functions. Although NOR and NAND gates are widely used in electronics, evolved circuits based on combinations of these gates are rare, thus suggesting that the strategy of combining the same basic logic gates might be inappropriate in order to easily implement synthetic computational constructs. The implications for future synthetic designs, the general view of synthetic biology as a standard engineering domain, as well as potencial drawbacks are outlined.

Chemical computing based on Turing patterns in two coupled cells with equal transport coefficients

Two diffusively coupled reaction cells with a nonlinear reaction are used to perform chemical computing based on targeted perturbations switching between two Turing patterns defining two states of a logical device.

Determinants of cell-to-cell variability in protein kinase signaling

Cells reliably sense environmental changes despite internal and external fluctuations, but the mechanisms underlying robustness remain unclear. We analyzed how fluctuations in signaling protein concentrations give rise to cell-to-cell variability in protein kinase signaling using analytical theory and numerical simulations. We characterized the dose-response behavior of signaling cascades by calculating the stimulus level at which a pathway responds (‘pathway sensitivity’) and the maximal activation level upon strong stimulation. Minimal kinase cascades with gradual dose-response behavior show strong variability, because the pathway sensitivity and the maximal activation level cannot be simultaneously invariant. Negative feedback regulation resolves this trade-off and coordinately reduces fluctuations in the pathway sensitivity and maximal activation. Feedbacks acting at different levels in the cascade control different aspects of the dose-response curve, thereby synergistically reducing the variability. We also investigated more complex, ultrasensitive signaling cascades capable of switch-like decision making, and found that these can be inherently robust to protein concentration fluctuations. We describe how the cell-to-cell variability of ultrasensitive signaling systems can be actively regulated, e.g., by altering the expression of phosphatase(s) or by feedback/feedforward loops. Our calculations reveal that slow transcriptional negative feedback loops allow for variability suppression while maintaining switch-like decision making. Taken together, we describe design principles of signaling cascades that promote robustness. Our results may explain why certain signaling cascades like the yeast pheromone pathway show switch-like decision making with little cell-to-cell variability.

Cells sense their surroundings and respond to soluble factors in the extracellular space. Extracellular factors frequently induce heterogeneous responses, thereby restricting the biological outcome to a fraction of the cell population. However, the question arises how such cell-to-cell variability can be controlled, because some cellular systems show a very homogenous response at a defined level of an extracellular stimulus. We derived an analytical framework to systematically characterize the cell-to-cell variability of intracellular signaling pathways which transduce external signals. We analyzed how heterogeneity arises from fluctuations in the total concentrations of signaling proteins because this is the main source of variability in eukaryotic systems. We find that signaling pathways can be highly variable or inherently invariant, depending on the kinetic parameters and the structural features of the cascade. Our results indicate that the cell-to-cell variability can be reduced by negative feedback in the cascade or by signaling crosstalk between parallel pathways. We precisely define the role of negative feedback loops in variability suppression, and show that different aspects of the dose-response curve can be controlled, depending on the feedback kinetics and site of action in the cascade. This work constitutes a first step towards a systematic understanding of cell-to-cell variability in signal transduction.

Control analysis of the eukaryotic cell cycle using gene copy-number series in yeast tetraploids

Background

In the model eukaryote, Saccharomyces cerevisiae, previous experiments have identified those genes that exert the most significant control over cell growth rate. These genes are termed HFC for high flux control. Such genes are overrepresented within pathways controlling the mitotic cell cycle.

Results

We postulated that the increase/decrease in growth rate is due to a change in the rate of progression through specific cell cycle steps. We extended and further developed an existing logical model of the yeast cell cycle in order elucidate how the HFC genes modulated progress through the cycle. This model can simulate gene dosage-variation and calculate the cycle time, determine the order and relative speed at which events occur, and predict arrests and failures to correctly execute a step. To experimentally test our model’s predictions, we constructed a tetraploid series of deletion mutants for a set of eight genes that control the G2/M transition. This system allowed us to vary gene copy number through more intermediate levels than previous studies and examine the impact of copy-number variation on growth, cell-cycle phenotype, and response to different cellular stresses.

Conclusions

For the majority of strains, the predictions agreed with experimental observations, validating our model and its use for further predictions. Where simulation and experiment diverged, we uncovered both novel tetraploid-specific phenotypes and a switch in the determinative execution point of a key cell-cycle regulator, the Cdc28 kinase, from the G1/S to the S/G2 boundaries.

Control of Turing patterns and their usage as sensors, memory arrays, and logic gates

We study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a two-variable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze the dependence of the system's steady states on varying rate coefficient of the recycling step while the coupling coefficients of the inhibitor and activator are fixed and set at the ratios 100:1, 1:1, and 4:5. We show that stable Turing patterns occur at all three ratios but, as expected, spontaneous transition from the spatially uniform steady state to the spatially nonuniform Turing patterns occurs only in the first case. The other two cases possess multiple Turing patterns, which are stabilized by secondary bifurcations and coexist with stable uniform periodic oscillations. For the 1:1 ratio we examine modular spatiotemporal perturbations, which allow for controllable switching between the uniform oscillations and various Turing patterns. Such modular perturbations are then used to construct chemical computing devices utilizing the multiple Turing patterns. By classifying various responses we propose: (a) a single-input resettable sensor capable of reading certain value of concentration, (b) two-input and three-input memory arrays capable of storing logic information, (c) three-input, three-output logic gates performing combinations of logical functions OR, XOR, AND, and NAND.

Amelioration of an undesired action of deguelin

The pharmaceutical world has greatly benefited from the well-characterized structure-function relationships of toxins with endogenous biomolecules, such as ion-channels, receptors, and signaling molecules. Thus, therapeutics derived from toxins have been aggressively pursued. However, the multifunctional role of various toxins may lead to undesirable off-target effects, hindering their use as therapeutic agents. In this paper, we suggest that previously unsuccessful toxins (due to off-target effects) may be revisited with mixtures by utilizing the pharmacodynamic response to the potential primary therapeutic as a starting point for finding new targets to ameliorate the unintended responses. In this proof of principle study, the pharmacodynamic response of HepG2 cells to a potential primary therapeutic (deguelin, a plant-derived chemopreventive agent) was monitored, and a possible secondary target (p38MAPK) was identified. As a single agent, deguelin decreased cellular viability at higher doses (>10 μM), but inhibited oxygen consumption over a wide dosing range (1.0-100 μM). Our results demonstrate that inhibition of oxygen consumption is related to an increase in p38MAPK phosphorylation, and may only be an undesired side effect of deguelin (i.e., one that does not contribute to the decrease in HepG2 viability). We further show that deguelin's negative effect on oxygen consumption can be diminished while maintaining efficacy when used as a therapeutic mixture with the judiciously selected secondary inhibitor (SB202190, p38MAPK inhibitor). These preliminary findings suggest that an endogenous response-directed mixtures approach, which uses a pharmacodynamic response to a primary therapeutic to determine a secondary target, allows previously unsuccessful toxins to be revisited as therapeutic mixtures.

Complexity of receptor tyrosine kinase signal processing

Our knowledge of molecular mechanisms of receptor tyrosine kinase (RTK) signaling advances with ever-increasing pace. Yet our understanding of how the spatiotemporal dynamics of RTK signaling control specific cellular outcomes has lagged behind. Systems-centered experimental and computational approaches can help reveal how overlapping networks of signal transducers downstream of RTKs orchestrate specific cell-fate decisions. We discuss how RTK network regulatory structures, which involve the immediate posttranslational and delayed transcriptional controls by multiple feed forward and feedback loops together with pathway cross talk, adapt cells to the combinatorial variety of external cues and conditions. This intricate network circuitry endows cells with emerging capabilities for RTK signal processing and decoding. We illustrate how mathematical modeling facilitates our understanding of RTK network behaviors by unraveling specific systems properties, including bistability, oscillations, excitable responses, and generation of intricate landscapes of signaling activities.

Robustness of signal transduction pathways

Signal transduction pathways transduce information about the outside of the cell to the nucleus, regulating gene expression and cell fate. To reliably inform the cell about its surroundings, information transfer has to be robust against typical perturbation that a cell experiences. Robustness of several mammalian signaling pathways has been studied recently by quantitative experimentation and using mathematical modeling. Here, we review these studies, and describe the emerging concepts of robustness and the underlying mechanisms.

Ultrasensitive response motifs: basic amplifiers in molecular signalling networks

Multi-component signal transduction pathways and gene regulatory circuits underpin integrated cellular responses to perturbations. A recurring set of network motifs serve as the basic building blocks of these molecular signalling networks. This review focuses on ultrasensitive response motifs (URMs) that amplify small percentage changes in the input signal into larger percentage changes in the output response. URMs generally possess a sigmoid input–output relationship that is steeper than the Michaelis–Menten type of response and is often approximated by the Hill function. Six types of URMs can be commonly found in intracellular molecular networks and each has a distinct kinetic mechanism for signal amplification. These URMs are: (i) positive cooperative binding, (ii) homo-multimerization, (iii) multistep signalling, (iv) molecular titration, (v) zero-order covalent modification cycle and (vi) positive feedback. Multiple URMs can be combined to generate highly switch-like responses. Serving as basic signal amplifiers, these URMs are essential for molecular circuits to produce complex nonlinear dynamics, including multistability, robust adaptation and oscillation. These dynamic properties are in turn responsible for higher-level cellular behaviours, such as cell fate determination, homeostasis and biological rhythm.

How scaffolds shape MAPK signaling: what we know and opportunities for systems approaches

Scaffolding proteins add a new layer of complexity to the dynamics of cell signaling. Above their basic function to bring several components of a signaling pathway together, recent experimental research has found that scaffolds influence signaling in a much more complex way: scaffolds can exert some catalytic function, influence signaling by allosteric mechanisms, are feedback-regulated, localize signaling activity to distinct regions of the cell or increase pathway fidelity. Here we review experimental and theoretical approaches that address the function of two MAPK scaffolds, Ste5, a scaffold of the yeast mating pathway and KSR1/2, a scaffold of the classical mammalian MAPK signaling pathway. For the yeast scaffold Ste5, detailed mechanistic models have been valuable for the understanding of its function. For scaffolds in mammalian signaling, however, models have been rather generic and sketchy. For example, these models predicted narrow optimal scaffold concentrations, but when revisiting these models by assuming typical concentrations, rather a range of scaffold levels optimally supports signaling. Thus, more realistic models are needed to understand the role of scaffolds in mammalian signal transduction, which opens a big opportunity for systems biology.

In vitro approach to predict post-translational phosphorylation response to mixtures

While exposure to chemical mixtures is an everyday reality, an understanding of their combined effects, and any potential prediction thereof, is extremely limited. Realistic exposures potentially consist of hundreds to thousands of chemicals per day, but even relatively simple binary mixture interactions can be inherently difficult to predict based upon the lack of temporal and spatial mechanisms for the individual constituents. To this end, we explore the concept of capitalizing on downstream convergence of intracellular signal transduction to experimentally simplify the means of determining xenobiotics that, when combined, could result in increased or unexpected toxicity. In a proof of principle study, we exposed HepG2 cells to deguelin, a natural isoflavonoid, alone and in combination with KCN, and determined the relative post-translational phosphorylation responses to several key proteins related to mitochondrial outer membrane permeabilization. Dose-dependent phosphorylation activity provides a clear identification of threshold response to low-level exposures, and crosstalk amongst selected proteins correctly forecasts mixtures interactions that may lead to increased toxicity. We then used Bliss Independence to determine if the experimentally measured mixture phosphorylation responses could be predicted with individual responses. Independence accurately predicted mixture interactions for deguelin and KCN (87.5%). To more fully exhaust independence as a model for determining potential pharmacodynamic interactions, we exposed HepG2 cells to deguelin and staurosporine, a broad kinase inhibitor; independence accurately predicted these mixture responses (77.5%). In this study, we demonstrate the potential of a new in vitro approach for the prediction of toxic mixtures interactions that is fundamentally driven by the interdependence of signal transduction and apoptosis.

Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise

BACKGROUND

Cell-to-cell variability in protein expression can be large, and its propagation through signaling networks affects biological outcomes. Here, we apply deterministic and probabilistic models and biochemical measurements to study how network topologies and cell-to-cell protein abundance variations interact to shape signaling responses.

RESULTS

We observe bimodal distributions of extracellular signal-regulated kinase (ERK) responses to epidermal growth factor (EGF) stimulation, which are generally thought to indicate bistable or ultrasensitive signaling behavior in single cells. Surprisingly, we find that a simple MAPK/ERK-cascade model with negative feedback that displays graded, analog ERK responses at a single cell level can explain the experimentally observed bimodality at the cell population level. Model analysis suggests that a conversion of graded input-output responses in single cells to digital responses at the population level is caused by a broad distribution of ERK pathway activation thresholds brought about by cell-to-cell variability in protein expression.

CONCLUSIONS

Our results show that bimodal signaling response distributions do not necessarily imply digital (ultrasensitive or bistable) single cell signaling, and the interplay between protein expression noise and network topologies can bring about digital population responses from analog single cell dose responses. Thus, cells can retain the benefits of robustness arising from negative feedback, while simultaneously generating population-level on/off responses that are thought to be critical for regulating cell fate decisions.

Computational approaches for analyzing information flow in biological networks

The advancements in "omics" (proteomics, genomics, lipidomics, and metabolomics) technologies have yielded large inventories of genes, transcripts, proteins, and metabolites. The challenge is to find out how these entities work together to regulate the processes by which cells respond to external and internal signals. Mathematical and computational modeling of signaling networks has a key role in this task, and network analysis provides insights into biological systems and has applications for medicine. Here, we review experimental and theoretical progress and future challenges toward this goal. We focus on how networks are reconstructed from data, how these networks are structured to control the flow of biological information, and how the design features of the networks specify biological decisions.

Membrane clustering and the role of rebinding in biochemical signaling

In many cellular signaling pathways, key components form clusters at the cell membrane. Although much work has focused on the mechanisms behind such cluster formation, the implications for downstream signaling remain poorly understood. Here, motivated by recent experiments, we use particle-based simulation to study a covalent modification network in which the activating component is either clustered or randomly distributed on the membrane. We find that whereas clustering reduces the response of a single-modification network, it can enhance the response of a double-modification network. The reduction is a bulk effect: a cluster presents a smaller effective target to a substrate molecule in the bulk. The enhancement, on the other hand, is a local effect: a cluster promotes the rapid rebinding and second activation of singly activated substrate molecules. As such, the enhancement relies on frequent collisions on a short timescale, leading to an optimal ratio of diffusion to association that agrees with typical measured rates. We complement simulation with analytic results at both the mean-field and first-passage distribution levels. Our results emphasize the importance of spatially resolved models, showing that significant effects of spatial correlations persist even in spatially averaged quantities such as response curves.

Modeling cortisol dynamics in the neuro-endocrine axis distinguishes normal, depression, and post-traumatic stress disorder (PTSD) in humans

Cortisol, secreted in the adrenal cortex in response to stress, is an informative biomarker that distinguishes anxiety disorders such as major depression and post-traumatic stress disorder (PTSD) from normal subjects. Yehuda et al. proposed a hypothesis that, in humans, the hypersensitive hypothalamus-pituitary-adrenal (HPA) axis is responsible for the occurrence of differing levels of cortisol in anxiety disorders. Specifically, PTSD subjects have lower cortisol levels during the late subjective night in comparison to normal subjects, and this was assumed to occur due to strong negative feedback loops in the HPA axis. In the present work, to address this hypothesis, we modeled the cortisol dynamics using nonlinear ordinary differential equations and estimated the kinetic parameters of the model to fit the experimental data of three categories, namely, normal, depressed, and PTSD human subjects. We concatenated the subjects (n = 3) in each category and created a model subject (n = 1) without considering the patient-to-patient variability in each case. The parameters of the model for the three categories were simultaneously obtained through global optimization. Bifurcation analysis carried out with the optimized parameters exhibited two supercritical Hopf points and, for the choice of parameters, the oscillations were found to be circadian in nature. The fitted kinetic parameters indicate that PTSD subjects have a strong negative feedback loop and, as a result, the predicted oscillating cortisol levels are extremely low at the nadir in contrast to normal subjects, albeit within the endocrinologic range. We also simulated the phenotypes for each of the categories and, as observed in the clinical data of PTSD patients, the simulated cortisol levels are consistently low at the nadir, and correspondingly the negative feedback was found to be extremely strong. These results from the model support the hypothesis that high stress intensity and strong negative feedback loop may cause hypersensitive neuro-endocrine axis that results in hypocortisolemia in PTSD.

PTSD is an anxiety disorder that occurs among persons exposed to a traumatic event involving life threat and injury. This is a co-morbid psychiatric disorder that occurs along with depression. Cortisol is an informative endocrine biomarker that can distinguish PTSD from other co-morbid disorders. In comparison to normal subjects, hypocortisolemia was observed during the night in PTSD, while hypercortisolemia was observed in depressed subjects. From analyzing the clinical data, Yehuda et al. hypothesized that hypocortisolemia in PTSD was due to the strong negative feedback loop operating in the neuroendocrine axis under severe stress. We complemented this hypothesis by constructing a mathematical model for cortisol dynamics in HPA axis and estimated the kinetic parameters that fitted the cortisol time series obtained from the clinical data of normal, depressed and PTSD patients. The parameters obtained from the simulated phenotypes also strongly support the hypothesis that, due to disruptive negative feedback loops, cortisol levels are different in normal, PTSD and depressed subjects during the night. Importantly, the model predicted the transitions from normal to various diseased states, and these transitions were shown to occur due to changes in the strength of the negative feedback loop and the stress intensity in the neuro-endocrine axis.

Adjusting phenotypes by noise control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.

Stochastic gene expression at the single cell level can lead to significant phenotypic variation at the population level. To obtain a desired phenotype, the noise levels of intracellular protein concentrations may need to be tuned and controlled. Noise levels often decrease in relative amount as the mean values increase. This implies that the noise levels can be passively controlled by changing the mean values. In an engineering perspective, the noise levels can be further controlled while the mean values can be simultaneously adjusted to desired values. Here, systematic schemes for such simultaneous control are described by identifying where and by how much the system needs to be perturbed. The schemes can be applied to the design process of a potential therapeutic HIV-drug that targets a certain set of reactions that are identified by the proposed analysis, to prevent stochastic transition to the lytic state. In some cases, the simultaneous control cannot be performed efficiently, when the noise levels strongly change with the mean values. This problem is shown to be resolved by applying extra noise and feedback.

Rule-based modeling of signal transduction: a primer

Biological cells accomplish their physiological functions using interconnected networks of genes, proteins, and other biomolecules. Most interactions in biological signaling networks, such as bimolecular association or covalent modification, can be modeled in a physically realistic manner using elementary reaction kinetics. However, the size and combinatorial complexity of such reaction networks have hindered such a mechanistic approach, leading many to conclude that it is premature and to adopt alternative statistical or phenomenological approaches. The recent development of rule-based modeling languages, such as BioNetGen (BNG) and Kappa, enables the precise and succinct encoding of large reaction networks. Coupled with complementary advances in simulation methods, these languages circumvent the combinatorial barrier and allow mechanistic modeling on a much larger scale than previously possible. These languages are also intuitive to the biologist and accessible to the novice modeler. In this chapter, we provide a self-contained tutorial on modeling signal transduction networks using the BNG Language and related software tools. We review the basic syntax of the language and show how biochemical knowledge can be articulated using reaction rules, which can be used to capture a broad range of biochemical and biophysical phenomena in a concise and modular way. A model of ligand-activated receptor dimerization is examined, with a detailed treatment of each step of the modeling process. Sections discussing modeling theory, implicit and explicit model assumptions, and model parameterization are included, with special focus on retaining biophysical realism and avoiding common pitfalls. We also discuss the more advanced case of compartmental modeling using the compartmental extension to BioNetGen. In addition, we provide a comprehensive set of example reaction rules that cover the various aspects of signal transduction, from signaling at the membrane to gene regulation. The reader can modify these reaction rules to model their own systems of interest.

GENERIC ENZYMATIC RATE EQUATION UNDER LIVING CONDITIONS

Based on our experience in kinetic modeling of coupled multiple metabolic pathways, we propose a generic rate equation for the dynamical modeling of metabolic kinetics. It is symmetric for forward and backward reactions. Its Michaelis-Menten-King-Altman form makes the kinetic parameters (or functions) easy to relate to experimental values in the database and to use in computation. In addition, such a uniform form is ready to arbitrary number of substrates and products with different stiochiometry. We explicitly show how to obtain such rate equations rigorously for three well-known binding mechanisms. Hence, the proposed rate equation is formally exact under the quasi-steady state condition. Various features of this generic rate equation are discussed. In particular, for irreversible reactions, the product inhibition which directly arises from enzymatic reaction is eliminated in a natural way. We also discuss how to include the effects of modifiers and cooperativity.

Load-induced modulation of signal transduction networks

Biological signal transduction networks are commonly viewed as circuits that pass along information--in the process amplifying signals, enhancing sensitivity, or performing other signal-processing tasks--to transcriptional and other components. Here, we report on a "reverse-causality" phenomenon, which we call load-induced modulation. Through a combination of analytical and experimental tools, we discovered that signaling was modulated, in a surprising way, by downstream targets that receive the signal and, in doing so, apply what in physics is called a load. Specifically, we found that non-intuitive changes in response dynamics occurred for a covalent modification cycle when load was present. Loading altered the response time of a system, depending on whether the activity of one of the enzymes was maximal and the other was operating at its minimal rate or whether both enzymes were operating at submaximal rates. These two conditions, which we call "limit regime" and "intermediate regime," were associated with increased or decreased response times, respectively. The bandwidth, the range of frequency in which the system can process information, decreased in the presence of load, suggesting that downstream targets participate in establishing a balance between noise-filtering capabilities and a circuit's ability to process high-frequency stimulation. Nodes in a signaling network are not independent relay devices, but rather are modulated by their downstream targets.

Biology using engineering tools: the negative feedback amplifier

Negative feedback is an ubiquitous feature of biological networks. Recent work from Sturm and colleaguespresents experimental evidence that biological negative feedback can serve the same function as it does for engineered systems: robustness to perturbations within the feedback loop. Such behavior has important implications for how to attack deregulated signaling networks containing negative feedback in diseases such as cancer.

Classification of cell signalling in tissue development

The traditional classification of signalling in biological systems is insufficient and outdated and novel efforts must take into account advances in systems theory, information theory and linguistics. We present some of the classification systems currently used both within and outside of the biological field and discuss some specific aspects of the nature of signalling in tissue development. The analytical methods used in understanding non-biological networks provide a valuable vocabulary, which requires integration and a system of classification to further facilitate development.

GIV/Girdin is a rheostat that fine-tunes growth factor signals during tumor progression

GIV/Girdin is a multidomain signaling molecule that enhances PI3K-Akt signals downstream of both G protein-coupled and growth factor receptors. We previously reported that GIV triggers cell migration via its C-terminal guanine-nucleotide exchange factor (GEF) motif that activates Gαi. Recently we discovered that GIV's C-terminus directly interacts with the epidermal growth factor receptor (EGFR), and when its GEF function is intact, a Gαi-GIV-EGFR signaling complex assembles. By coupling G proteins to growth factor receptors, GIV is uniquely poised to intercept the incoming receptor-initiated signals and modulate them via G protein intermediates. Subsequent work has revealed that expression of the highly specialized C-terminus of GIV undergoes a bipartite dysregulation during oncogenesis-full length GIV with an intact C-terminus is expressed at levels ~20-50-fold above normal in highly invasive cancer cells and metastatic tumors, but its C-terminus is truncated by alternative splicing in poorly invasive cancer cells and non-invasive tumors. The consequences of such dysregulation on graded signal transduction and cellular phenotypes in the normal epithelium and its implication during tumor progression are discussed herein. Based on the fact that GIV grades incoming signals initiated by ligand-activated receptors by linking them to cyclical activation of G proteins, we propose that GIV is a molecular rheostat for signal transduction.