Feedback loops shape cellular signals in space and time

Chemotaxis: a feedback-based computational model robustly predicts multiple aspects of real cell behaviour

A simple feedback model of chemotaxis explains how new pseudopods are made and how eukaryotic cells steer toward chemical gradients.

The mechanism of eukaryotic chemotaxis remains unclear despite intensive study. The most frequently described mechanism acts through attractants causing actin polymerization, in turn leading to pseudopod formation and cell movement. We recently proposed an alternative mechanism, supported by several lines of data, in which pseudopods are made by a self-generated cycle. If chemoattractants are present, they modulate the cycle rather than directly causing actin polymerization. The aim of this work is to test the explanatory and predictive powers of such pseudopod-based models to predict the complex behaviour of cells in chemotaxis. We have now tested the effectiveness of this mechanism using a computational model of cell movement and chemotaxis based on pseudopod autocatalysis. The model reproduces a surprisingly wide range of existing data about cell movement and chemotaxis. It simulates cell polarization and persistence without stimuli and selection of accurate pseudopods when chemoattractant gradients are present. It predicts both bias of pseudopod position in low chemoattractant gradients and—unexpectedly—lateral pseudopod initiation in high gradients. To test the predictive ability of the model, we looked for untested and novel predictions. One prediction from the model is that the angle between successive pseudopods at the front of the cell will increase in proportion to the difference between the cell's direction and the direction of the gradient. We measured the angles between pseudopods in chemotaxing Dictyostelium cells under different conditions and found the results agreed with the model extremely well. Our model and data together suggest that in rapidly moving cells like Dictyostelium and neutrophils an intrinsic pseudopod cycle lies at the heart of cell motility. This implies that the mechanism behind chemotaxis relies on modification of intrinsic pseudopod behaviour, more than generation of new pseudopods or actin polymerization by chemoattractants.

The efficiency, sensitivity, and huge dynamic range of eukaryotic cell chemotaxis have proven very hard to explain. Cells respond to shallow gradients of chemotactic molecules with directed movement, but the mechanisms remain elusive. Most current models predict that cells have an internal “compass” produced by processing the extracellular signal into an intracellular mechanism that points the cell towards the gradient and steers it in that direction. In this article, we present evidence that this internal compass does not exist; instead, the cell orients itself simply by making use of its pseudopods—the dynamic finger-like projections on the surface of the cell. We approached the question by making a computational model of the movement of a cell without a compass. In this model, the cell moves in a convincingly natural way simply by using its pseudopods, which respond to positive- and negative-feedback loops. The concentration of the chemoattractant molecule modulates the amount of positive feedback. Apart from this, no signal processing is necessary. This simple model reproduces many observations about normal chemotaxis. It also accurately predicts the angle at which new pseudopods split off from old ones, which had not been previously measured. The computational model thus demonstrates that pseudopod-based mechanisms are powerful enough to explain chemotaxis.

Polarized notum activation at wounds inhibits Wnt function to promote planarian head regeneration

Regeneration requires initiation of programs tailored to the identity of missing parts. Head-versus-tail regeneration in planarians presents a paradigm for study of this phenomenon. After injury, Wnt signaling promotes tail regeneration. We report that wounding elicits expression of the Wnt inhibitor notum preferentially at anterior-facing wounds. This expression asymmetry occurs at essentially any wound, even if the anterior pole is intact. Inhibition of notum with RNA interference (RNAi) causes regeneration of an anterior-facing tail instead of a head, and double-RNAi experiments indicate that notum inhibits Wnt signaling to promote head regeneration. notum expression is itself controlled by Wnt signaling, suggesting that regulation of feedback inhibition controls the binary head-tail regeneration outcome. We conclude that local detection of wound orientation with respect to tissue axes results in distinct signaling environments that initiate appropriate regeneration responses.

A comparison of mathematical models for polarization of single eukaryotic cells in response to guided cues

Polarization, a primary step in the response of an individual eukaryotic cell to a spatial stimulus, has attracted numerous theoretical treatments complementing experimental studies in a variety of cell types. While the phenomenon itself is universal, details differ across cell types, and across classes of models that have been proposed. Most models address how symmetry breaking leads to polarization, some in abstract settings, others based on specific biochemistry. Here, we compare polarization in response to a stimulus (e.g., a chemoattractant) in cells typically used in experiments (yeast, amoebae, leukocytes, keratocytes, fibroblasts, and neurons), and, in parallel, responses of several prototypical models to typical stimulation protocols. We find that the diversity of cell behaviors is reflected by a diversity of models, and that some, but not all models, can account for amplification of stimulus, maintenance of polarity, adaptation, sensitivity to new signals, and robustness.

Plant systems biology: network matters

Systems biology is all about networks. A recent trend has been to associate systems biology exclusively with the study of gene regulatory or protein-interaction networks. However, systems biology approaches can be applied at many other scales, from the subatomic to the ecosystem scales. In this review, we describe studies at the sub-cellular, tissue, whole plant and crop scales and highlight how these studies can be related to systems biology. We discuss the properties of system approaches at each scale as well as their current limits, and pinpoint in each case advances unique to the considered scale but representing potential for the other scales. We conclude by examining plant models bridging different scales and considering the future prospects of plant systems biology.

On the architecture of cell regulation networks

BACKGROUND

With the rapid development of high-throughput experiments, detecting functional modules has become increasingly important in analyzing biological networks. However, the growing size and complexity of these networks preclude structural breaking in terms of simplest units. We propose a novel graph theoretic decomposition scheme combined with dynamics consideration for probing the architecture of complex biological networks.

RESULTS

Our approach allows us to identify two structurally important components: the "minimal production unit"(MPU) which responds quickly and robustly to external signals, and the feedback controllers which adjust the output of the MPU to desired values usually at a larger time scale. The successful application of our technique to several of the most common cell regulation networks indicates that such architectural feature could be universal. Detailed illustration and discussion are made to explain the network structures and how they are tied to biological functions.

CONCLUSIONS

The proposed scheme may be potentially applied to various large-scale cell regulation networks to identify functional modules that play essential roles and thus provide handles for analyzing and understanding cell activity from basic biochemical processes.

Hindbrain patterning requires fine-tuning of early krox20 transcription by Sprouty 4

Vertebrate hindbrain segmentation is an evolutionarily conserved process that involves a complex interplay of transcription factors and signalling pathways. Fibroblast growth factor (FGF) signalling plays a major role, notably by controlling the expression of the transcription factor Krox20 (Egr2), which is required for the formation and specification of two segmental units: rhombomeres (r) 3 and 5. Here, we explore the molecular mechanisms downstream of FGF signalling and the function of Sprouty 4 (Spry4), a negative-feedback regulator of this pathway, in zebrafish. We show that precise modulation of FGF signalling by Spry4 is required to determine the appropriate onset of krox20 transcription in r3 and r5 and, ultimately, rhombomere size in the r3-r5 region. FGF signalling acts by modulating the activity of krox20 initiator enhancer elements B and C; in r5, we show that this regulation is mediated by direct binding of the transcription factor MafB to element B. By contrast, FGF signalling does not control the krox20 autoregulatory element A, which is responsible for amplification and maintenance of krox20 expression. Therefore, early krox20 transcription sets the blueprint for r3-r5 patterning. This work illustrates the necessity for fine-tuning in a common and fundamental patterning process, based on a bistable cell-fate choice involving the coupling of an extracellular gradient with a positive-feedback loop. In this mode of patterning, precision and robustness can be achieved by the introduction of a negative-feedback loop, which, in the hindbrain, is mediated by Spry4.

Only signaling modules that discriminate sharply between stimulatory and nonstimulatory inputs require basal signaling for fast cellular responses

In many types of cells, binding of molecules to their receptors enables cascades of intracellular chemical reactions to take place (signaling). However, a low level of signaling also occurs in most unstimulated cells. Such basal signaling in resting cells can have many functions, one of which is that it is thought to be required for fast cellular responses to external stimuli. A mechanistic understanding of why this is true and which features of cellular signaling networks make basal signaling necessary for fast responses is unknown. We address this issue by obtaining the time required for activation of common types of cell signaling modules with and without basal signaling. Our results show that the absence of basal signaling does not have any dramatic effects on the response time for signaling modules that exhibit a graded response to increasing stimulus levels. In sharp contrast, signaling modules that exhibit sharp dose-response curves which discriminate sensitively between stimuli to which the cell needs to respond and low-grade inputs (or stochastic noise) require basal signaling for fast cellular responses. In such cases, we find that an optimal level of basal signaling balances the requirements for fast cellular responses while minimizing spurious activation without appropriate stimulation.

Context, specificity, and self-organization in auxin response

Auxin is a simple molecule with a remarkable ability to control plant growth, differentiation, and morphogenesis. The mechanistic basis for this versatility appears to stem from the highly complex nature of the networks regulating auxin metabolism, transport and response. These heavily feedback-regulated and inter-dependent mechanisms are complicated in structure and complex in operation giving rise to a system with self-organizing properties capable of generating highly context-specific responses to auxin as a single, generic signal.

Computational systems biology of aging

Computational systems biology is expected to make major contributions to unravel the complex molecular mechanisms underlying the progression of aging in cells, tissues, and organisms. The development of computational approaches is, however, challenged by a wide spectrum of aging mechanisms participating on different levels of biological organization. The tight connectivity between the molecular constituents, functions, and cell states requires frameworks and strategies that extend beyond current practice to model, simulate, and predict the progression of aging and the emerging aging phenotypes. We provide a general overview of the specific computational tasks and opportunities in aging research, and discuss some illustrative systems level concepts in more detail. One example provided here is the assembly of a conceptual whole cell model that considers the temporal dynamics of the aging process grounded on molecular mechanisms. Another application is the assembly of interactomes, such as protein networks that allow us to analyze changes in network topology and interaction of proteins that have been implicated in aging with other cellular constituents and processes. We introduce the necessary key steps to build these applications and discuss their merits and future extensions for aging research. WIREs Syst Biol Med 2011 3 414-428 DOI: 10.1002/wsbm.126

A conceptual molecular network for chemotactic behaviors characterized by feedback of molecules cycling between the membrane and the cytosol

Cell chemotaxis has been characterized as the formation of a front-back axis that is triggered by a gradient of chemoattractant; however, chemotaxis is accompanied by more complicated behaviors. These include migration in a straight line with a stable axis [the stable single-axis (SSA) pattern] and repeated splitting of the leading edge of the cell into two regions, followed by the "choice" of one of these as the new leading edge [the split and choice (S&C) pattern]. Indeed, transition between these two behaviors can be observed in individual cells. However, the conceptual framework of the network of signaling molecules that generates these patterns remains to be clarified. We confirmed theoretically that a system that has positive and negative feedback loops involving the reciprocal cycling between the membrane and the cytosol of molecules that promote membrane protrusion or retraction generates SSA and S&C patterns of migratory behavior under similar conditions. We also predicted properties of the instabilities of such a system, which are essential for the generation of these behaviors, and we verified their existence in chemotaxing cells. Our research provides a simple model of network structure for chemotactic behaviors, including cell polarization.

Systems analysis of small signaling modules relevant to eight human diseases

Using eight newly generated models relevant to addiction, Alzheimer’s disease, cancer, diabetes, HIV, heart disease, malaria, and tuberculosis, we show that systems analysis of small (4–25 species), bounded protein signaling modules rapidly generates new quantitative knowledge from published experimental research. For example, our models show that tumor sclerosis complex (TSC) inhibitors may be more effective than the rapamycin (mTOR) inhibitors currently used to treat cancer, that HIV infection could be more effectively blocked by increasing production of the human innate immune response protein APOBEC3G, rather than targeting HIV’s viral infectivity factor (Vif), and how peroxisome proliferator-activated receptor alpha (PPARα) agonists used to treat dyslipidemia would most effectively stimulate PPARα signaling if drug design were to increase agonist nucleoplasmic concentration, as opposed to increasing agonist binding affinity for PPARα. Comparative analysis of system-level properties for all eight modules showed that a significantly higher proportion of concentration parameters fall in the top 15th percentile sensitivity ranking than binding affinity parameters. In infectious disease modules, host networks were significantly more sensitive to virulence factor concentration parameters compared to all other concentration parameters. This work supports the future use of this approach for informing the next generation of experimental roadmaps for known diseases.

Oscillatory control of signalling molecules

The emergence of biological function from the dynamic control of cellular signalling molecules is a fundamental process in biology. Key questions include: How do cells decipher noisy environmental cues, encode these signals to control fate decisions and propagate information through tissues? Recent advances in systems biology, and molecular and cellular biology, exemplified by analyses of signalling via the transcription factor Nuclear Factor kappaB (NF-κB), reveal a critical role of oscillatory control in the regulation of these biological functions. The emerging view is that the oscillatory dynamics of signalling molecules and the epigenetically regulated specificity for target genes contribute to robust regulation of biological function at different levels of cellular organisation through frequency-dependent information encoding.

Kinetic studies of the Arf activator Arno on model membranes in the presence of Arf effectors suggest control by a positive feedback loop

Proteins of the cytohesin/Arno/Grp1 family of Arf activators are positive regulators of the insulin-signaling pathway and control various remodeling events at the plasma membrane. Arno has a catalytic Sec7 domain, which promotes GDP to GTP exchange on Arf, followed by a pleckstrin homology (PH) domain. Previous studies have revealed two functions of the PH domain: inhibition of the Sec7 domain and membrane targeting. Interestingly, the Arno PH domain interacts not only with a phosphoinositide (phosphatidylinositol 4,5-bisphosphate or phosphatidylinositol 3,4,5-trisphosphate) but also with an activating Arf family member, such as Arf6 or Arl4. Using the full-length membrane-bound forms of Arf1 and Arf6 instead of soluble forms, we show here that the membrane environment dramatically affects the mechanism of Arno activation. First, Arf6-GTP stimulates Arno at nanomolar concentrations on liposomes compared with micromolar concentrations in solution. Second, mutations in the PH domain that abolish interaction with Arf6-GTP render Arno completely inactive when exchange reactions are reconstituted on liposomes but have no effect on Arno activity in solution. Third, Arno is activated by its own product Arf1-GTP in addition to a distinct activating Arf isoform. Consequently, Arno activity is strongly modulated by competition with Arf effectors. These results show that Arno behaves as a bistable switch, having an absolute requirement for activation by an Arf protein but, once triggered, becoming highly active through the positive feedback effect of Arf1-GTP. This property of Arno might provide an explanation for its function in signaling pathways that, once triggered, must move forward decisively.

Confidence from uncertainty--a multi-target drug screening method from robust control theory

Background

Robustness is a recognized feature of biological systems that evolved as a defence to environmental variability. Complex diseases such as diabetes, cancer, bacterial and viral infections, exploit the same mechanisms that allow for robust behaviour in healthy conditions to ensure their own continuance. Single drug therapies, while generally potent regulators of their specific protein/gene targets, often fail to counter the robustness of the disease in question. Multi-drug therapies offer a powerful means to restore disrupted biological networks, by targeting the subsystem of interest while preventing the diseased network from reconciling through available, redundant mechanisms. Modelling techniques are needed to manage the high number of combinatorial possibilities arising in multi-drug therapeutic design, and identify synergistic targets that are robust to system uncertainty.

Results

We present the application of a method from robust control theory, Structured Singular Value or μ- analysis, to identify highly effective multi-drug therapies by using robustness in the face of uncertainty as a new means of target discrimination. We illustrate the method by means of a case study of a negative feedback network motif subject to parametric uncertainty.

Conclusions

The paper contributes to the development of effective methods for drug screening in the context of network modelling affected by parametric uncertainty. The results have wide applicability for the analysis of different sources of uncertainty like noise experienced in the data, neglected dynamics, or intrinsic biological variability.

Systematic quantification of negative feedback mechanisms in the extracellular signal-regulated kinase (ERK) signaling network

Cell responses are actuated by tightly controlled signal transduction pathways. Although the concept of an integrated signaling network replete with interpathway cross-talk and feedback regulation is broadly appreciated, kinetic data of the type needed to characterize such interactions in conjunction with mathematical models are lacking. In mammalian cells, the Ras/ERK pathway controls cell proliferation and other responses stimulated by growth factors, and several cross-talk and feedback mechanisms affecting its activation have been identified. In this work, we take a systematic approach to parse the magnitudes of multiple regulatory mechanisms that attenuate ERK activation through canonical (Ras-dependent) and non-canonical (PI3K-dependent) pathways. In addition to regulation of receptor and ligand levels, we consider three layers of ERK-dependent feedback: desensitization of Ras activation, negative regulation of MEK kinase (e.g. Raf) activities, and up-regulation of dual-specificity ERK phosphatases. Our results establish the second of these as the dominant mode of ERK self-regulation in mouse fibroblasts. We further demonstrate that kinetic models of signaling networks, trained on a sufficient diversity of quantitative data, can be reasonably comprehensive, accurate, and predictive in the dynamical sense.

The pursuit of oncotargets through understanding defective cell regulation

More effective anticancer agents are essential, as has too often been demonstrated by the paucity of therapeutics which preserve life. Their discovery is very difficult. Many approaches are being applied, from testing folk medicines to automated high throughput screening of large chemical libraries. Mutations in cancer cells create dysfunctional regulatory systems. This Perspective summarizes an approach to applying defective molecular control mechanisms as oncotargets on which drug discoveries against cancer can be based.

The pursuit of oncotargets through understanding defective cell regulation

More effective anticancer agents are essential, as has too often been demonstrated by the paucity of therapeutics which preserve life. Their discovery is very difficult. Many approaches are being applied, from testing folk medicines to automated high throughput screening of large chemical libraries. Mutations in cancer cells create dysfunctional regulatory systems. This Perspective summarizes an approach to applying defective molecular control mechanisms as oncotargets on which drug discoveries against cancer can be based.

Single-cell and coupled GRN models of cell patterning in the Arabidopsis thaliana root stem cell niche

BACKGROUND

Recent experimental work has uncovered some of the genetic components required to maintain the Arabidopsis thaliana root stem cell niche (SCN) and its structure. Two main pathways are involved. One pathway depends on the genes SHORTROOT and SCARECROW and the other depends on the PLETHORA genes, which have been proposed to constitute the auxin readouts. Recent evidence suggests that a regulatory circuit, composed of WOX5 and CLE40, also contributes to the SCN maintenance. Yet, we still do not understand how the niche is dynamically maintained and patterned or if the uncovered molecular components are sufficient to recover the observed gene expression configurations that characterize the cell types within the root SCN. Mathematical and computational tools have proven useful in understanding the dynamics of cell differentiation. Hence, to further explore root SCN patterning, we integrated available experimental data into dynamic Gene Regulatory Network (GRN) models and addressed if these are sufficient to attain observed gene expression configurations in the root SCN in a robust and autonomous manner.

RESULTS

We found that an SCN GRN model based only on experimental data did not reproduce the configurations observed within the root SCN. We developed several alternative GRN models that recover these expected stable gene configurations. Such models incorporate a few additional components and interactions in addition to those that have been uncovered. The recovered configurations are stable to perturbations, and the models are able to recover the observed gene expression profiles of almost all the mutants described so far. However, the robustness of the postulated GRNs is not as high as that of other previously studied networks.

CONCLUSIONS

These models are the first published approximations for a dynamic mechanism of the A. thaliana root SCN cellular pattering. Our model is useful to formally show that the data now available are not sufficient to fully reproduce root SCN organization and genetic profiles. We then highlight some experimental holes that remain to be studied and postulate some novel gene interactions. Finally, we suggest the existence of a generic dynamical motif that can be involved in both plant and animal SCN maintenance.

Crosstalk between insulin receptor and G protein-coupled receptor signaling systems leads to Ca²+ oscillations in pancreatic cancer PANC-1 cells

We examined crosstalk between the insulin receptor and G protein-coupled receptor (GPCR) signaling pathways in individual human pancreatic cancer PANC-1 cells. Treatment of cells with insulin (10 ng/ml) for 5 min markedly enhanced the proportion of cells that display an increase in intracellular [Ca²+] induced by picomolar concentrations of the GPCR agonist neurotensin. Interestingly, insulin increased the proportion of a subpopulation of cells that exhibit intracellular [Ca²+] oscillations in response to neurotensin at concentrations as low as 50-200 pM. Insulin enhanced GPCR-induced Ca²+ signaling in a time- and dose-dependent manner; a marked potentiation was obtained after an exposure to a concentration of 10 ng/ml for 5 min. Treatment with the mTORC1 inhibitor rapamycin abrogated the increase in GPCR-induced [Ca²+](i) oscillations produced by insulin. Our results identify a novel aspect in the crosstalk between insulin receptor and GPCR signaling systems in pancreatic cancer cells, namely that insulin increases the number of [Ca²+](i) oscillating cells induced by physiological concentrations of GPCR agonists through an mTORC1-dependent pathway.

Microfluidic technologies for temporal perturbations of chemotaxis

Most cells in the body have the ability to change their physical locations during physiologic or pathologic events such as inflammation, wound healing, or cancer. When cell migration is directed toward sources of cue chemicals, the process is known as chemotaxis, and it requires linking the sensing of chemicals through receptors on the surfaces of the cells to the directional activation of the motility apparatus inside the cells. This link is supported by complex intracellular signaling pathways, and although details regarding the nature of the molecules involved in the signal transduction are well established, far less is known about how different signaling molecules and processes are dynamically interconnected and how slower and faster signaling events take place simultaneously inside moving cells. In this context, advances in microfluidic technologies are enabling the emergence of new tools that facilitate the development of experimental protocols in which the cellular microenvironment is precisely controlled in time and space and in which signaling-associated changes inside cells can be quantitatively measured and compared. These tools could enable new insights into the intricacies of the biological systems that participate in chemotaxis processes and could have the potential to accelerate the development of novel therapeutic strategies to control cell motility and enhance our abilities for medical intervention during health and disease.

Beyond the wiring diagram: signalling through complex neuromodulator networks

During the computations performed by the nervous system, its 'wiring diagram'--the map of its neurons and synaptic connections--is dynamically modified and supplemented by multiple actions of neuromodulators that can be so complex that they can be thought of as constituting a biochemical network that combines with the neuronal network to perform the computation. Thus, the neuronal wiring diagram alone is not sufficient to specify, and permit us to understand, the computation that underlies behaviour. Here I review how such modulatory networks operate, the problems that their existence poses for the experimental study and conceptual understanding of the computations performed by the nervous system, and how these problems may perhaps be solved and the computations understood by considering the structural and functional 'logic' of the modulatory networks.

Different roles of G protein subunits beta1 and beta2 in neutrophil function revealed by gene expression silencing in primary mouse neutrophils

Neutrophils play important roles in host innate immunity and various inflammation-related diseases. In addition, neutrophils represent an excellent system for studying directional cell migration. However, neutrophils are terminally differentiated cells that are short lived and refractory to transfection; thus, they are not amenable for existing gene silencing techniques. Here we describe the development of a method to silence gene expression efficiently in primary mouse neutrophils. A mouse stem cell virus-based retroviral vector was modified to express short hairpin RNAs and fluorescent marker protein at high levels in hematopoietic cells and used to infect mouse bone marrow cells prior to reconstitution of the hematopoietic system in lethally irradiated mice. This method was used successfully to silence the expression of Gbeta(1) and/or Gbeta(2) in mouse neutrophils. Knockdown of Gbeta(2) appeared to affect primarily the directionality of neutrophil chemotaxis rather than motility, whereas knockdown of Gbeta(1) had no significant effect. However, knockdown of both Gbeta(1) and Gbeta(2) led to significant reduction in motility and responsiveness. In addition, knockdown of Gbeta(1) but not Gbeta(2) inhibited the ability of neutrophils to kill ingested bacteria, and only double knockdown resulted in significant reduction in bacterial phagocytosis. Therefore, we have developed a short hairpin RNA-based method to effectively silence gene expression in mouse neutrophils for the first time, which allowed us to uncover divergent roles of Gbeta(1) and Gbeta(2) in the regulation of neutrophil functions.

Structure of the EGF receptor transactivation circuit integrates multiple signals with cell context

Transactivation of the epidermal growth factor receptor (EGFR) is thought to be a process by which a variety of cellular inputs can be integrated into a single signaling pathway through either stimulated proteolysis (shedding) of membrane-anchored EGFR ligands or by modification of the activity of the EGFR. As a first step towards building a predictive model of the EGFR transactivation circuit, we quantitatively defined how signals from multiple agonists were integrated both upstream and downstream of the EGFR to regulate extracellular signal regulated kinase (ERK) activity in human mammary epithelial cells. By using a "non-binding" reporter of ligand shedding, we found that transactivation triggers a positive feedback loop from ERK back to the EGFR such that ligand shedding drives EGFR-stimulated ERK that in turn drives further ligand shedding. Importantly, activated Ras and ERK levels were nearly linear functions of ligand shedding and the effect of multiple, sub-saturating inputs was additive. Simulations showed that ERK-mediated feedback through ligand shedding resulted in a stable steady-state level of activated ERK, but also showed that the extracellular environment can modulate the level of feedback. Our results suggest that the transactivation circuit acts as a context-dependent integrator and amplifier of multiple extracellular signals and that signal integration can effectively occur at multiple points in the EGFR pathway.

Systems biology and modeling in neuroblastoma: practicalities and perspectives

Neuroblastoma (NB) is a common pediatric malignancy characterized by clinical and biological heterogeneity. A host of prognostic markers are available, contributing to accurate risk stratification and appropriate treatment allocation. Unfortunately, outcome is still poor for many patients, indicating the need for a new approach with enhanced utilization of the available biological data. Systems biology is a holistic approach in which all components of a biological system carry equal importance. Systems biology uses mathematical modeling and simulation to investigate dynamic interactions between system components, as a means of explaining overall system behavior. Systems biology can benefit the biomedical sciences by providing a more complete understanding of human disease, enhancing the development of targeted therapeutics. Systems biology is largely contiguous with current approaches in NB, which already employ an integrative and pseudo-holistic approach to disease management. Systems modeling of NB offers an optimal method for continuing progression in this field, and conferring additional benefit to current risk stratification and management. Likewise, NB provides an opportunity for systems biology to prove its utility in the context of human disease, since the biology of NB is comprehensively characterized and, therefore, suited to modeling. The purpose of this review is to outline the benefits, challenges and fundamental workings of systems modeling in human disease, using a specific example of bottom-up modeling in NB. The intention is to demonstrate practical requirements to begin bridging the gap between biological research and applied mathematical approaches for the mutual gain of both fields, and with additional benefits for clinical management.

Positive autoregulation shapes response timing and intensity in two-component signal transduction systems

Positive feedback loops are regulatory elements that can modulate expression output, kinetics and noise in genetic circuits. Transcriptional regulators participating in such loops are often expressed from two promoters, one constitutive and one autoregulated. Here, we investigate the interplay of promoter strengths and the intensity of the stimulus activating the transcriptional regulator in defining the output of a positively autoregulated genetic circuit. Using a mathematical model of two-component regulatory systems, which are present in all domains of life, we establish that positive feedback strongly affects the steady-state output levels at both low and high levels of stimulus if the constitutive promoter of the regulator is weak. By contrast, the effect of positive feedback is negligible when the constitutive promoter is sufficiently strong, unless the stimulus intensity is very high. Furthermore, we determine that positive feedback can affect both transient and steady state output levels even in the simplest genetic regulatory systems. We tested our modeling predictions by abolishing the positive feedback loop in the two-component regulatory system PhoP/PhoQ of Salmonella enterica, which resulted in diminished induction of PhoP-activated genes.

Population robustness arising from cellular heterogeneity

Heterogeneity between individual cells is a common feature of dynamic cellular processes, including signaling, transcription, and cell fate; yet the overall tissue level physiological phenotype needs to be carefully controlled to avoid fluctuations. Here we show that in the NF-kappaB signaling system, the precise timing of a dual-delayed negative feedback motif [involving stochastic transcription of inhibitor kappaB (IkappaB)-alpha and -epsilon] is optimized to induce heterogeneous timing of NF-kappaB oscillations between individual cells. We suggest that this dual-delayed negative feedback motif enables NF-kappaB signaling to generate robust single cell oscillations by reducing sensitivity to key parameter perturbations. Simultaneously, enhanced cell heterogeneity may represent a mechanism that controls the overall coordination and stability of cell population responses by decreasing temporal fluctuations of paracrine signaling. It has often been thought that dynamic biological systems may have evolved to maximize robustness through cell-to-cell coordination and homogeneity. Our analyses suggest in contrast, that this cellular variation might be advantageous and subject to evolutionary selection. Alternative types of therapy could perhaps be designed to modulate this cellular heterogeneity.

Rule-based cell systems model of aging using feedback loop motifs mediated by stress responses

Investigating the complex systems dynamics of the aging process requires integration of a broad range of cellular processes describing damage and functional decline co-existing with adaptive and protective regulatory mechanisms. We evolve an integrated generic cell network to represent the connectivity of key cellular mechanisms structured into positive and negative feedback loop motifs centrally important for aging. The conceptual network is casted into a fuzzy-logic, hybrid-intelligent framework based on interaction rules assembled from a priori knowledge. Based upon a classical homeostatic representation of cellular energy metabolism, we first demonstrate how positive-feedback loops accelerate damage and decline consistent with a vicious cycle. This model is iteratively extended towards an adaptive response model by incorporating protective negative-feedback loop circuits. Time-lapse simulations of the adaptive response model uncover how transcriptional and translational changes, mediated by stress sensors NF-κB and mTOR, counteract accumulating damage and dysfunction by modulating mitochondrial respiration, metabolic fluxes, biosynthesis, and autophagy, crucial for cellular survival. The model allows consideration of lifespan optimization scenarios with respect to fitness criteria using a sensitivity analysis. Our work establishes a novel extendable and scalable computational approach capable to connect tractable molecular mechanisms with cellular network dynamics underlying the emerging aging phenotype.

The global process of aging disturbs a broad range of cellular mechanisms in a complex fashion and is not well understood. One important goal of computational approaches in aging is to develop integrated models in terms of a unifying aging theory, predicting progression of aging phenotypes grounded on molecular mechanisms. However, current experimental data incoherently reflects many isolated processes from a large diversity of approaches, biological model systems, and species, which makes such integration a challenging task. In an attempt to close this gap, we iteratively develop a fuzzy-logic cell systems model considering the interplay of damage, metabolism, and signaling by positive and negative feedback-loop motifs using relationships drawn from literature data. Because cellular biodynamics may be considered a complex control system, this approach seems particularly suitable. Here, we demonstrate that rule-based fuzzy-logic models provide semi-quantitative predictions that enhance our understanding of complex and interlocked molecular mechanisms and their implications on the aging physiome.

Lose and gain: impacts of ERK5 and JNK cascades on each other

Kinase cascades in ERK5 (Extracellular signal-regulated kinases) and JNK (c-Jun N-terminal kinases) signaling pathways mediate the sensing and processing of stimuli. Cross-talks between signaling cascades is a likely phenomenon that can cause apparently different biological responses from a single pathway, on its activation. Feedback loops have the potential to greatly alter the properties of a pathway and its response to stimuli. Based on enzyme kinetic reactions, mathematical models have been developed to predict and analyze the impacts of cross-talks and feedback loops in ERK5 and JNK cascades. It has been observed that, there is no significant impact on neither ERK5 activation nor JNKs' activation due to cross-talks between them. But it is due to cross-talks and feedback loops in ERK5 and JNK cascade, ERK5 gets activated in a transient manner in the absence of input signals. Planning to obtain the parameter values from the experimentalist and the result should be validated by experimental verification.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-010-9061-4) contains supplementary material, which is available to authorized users.

Understanding eukaryotic chemotaxis: a pseudopod-centred view

Current descriptions of eukaryotic chemotaxis and cell movement focus on how extracellular signals (chemoattractants) cause new pseudopods to form. This 'signal-centred' approach is widely accepted but is derived mostly from special cases, particularly steep chemoattractant gradients. I propose a 'pseudopod-centred' explanation, whereby most pseudopods form themselves, without needing exogenous signals, and chemoattractants only bias internal pseudopod dynamics. This reinterpretation of recent data suggests that future research should focus on pseudopod mechanics, not signal processing.

A critical quantity for noise attenuation in feedback systems

Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as "signed activation time". We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.

A formal model for analyzing drug combination effects and its application in TNF-alpha-induced NFkappaB pathway

Background

Drug combination therapy is commonly used in clinical practice. Many methods including Bliss independence method have been proposed for drug combination design based on simulations models or experiments. Although Bliss independence method can help to solve the drug combination design problem when there are only a small number of combinations, as the number of combinations increases, it may not be scalable. Exploration of system structure becomes important to reduce the complexity of the design problem.

Results

In this paper, we deduced a mathematical model which can simplify the serial structure and parallel structure of biological pathway for synergy evaluation of drug combinations. We demonstrated in steady state the sign of the synergism assessment factor derivative of the original system can be predicted by the sign of its simplified system. In addition, we analyzed the influence of feedback structure on survival ratio of the serial structure. We provided a sufficient condition under which the combination effect could be maintained. Furthermore, we applied our method to find three synergistic drug combinations on tumor necrosis factor α-induced NFκB pathway and subsequently verified by the cell experiment.

Conclusions

We identified several structural properties underlying the Bliss independence criterion, and developed a systematic simplification framework for drug combiation desgin by combining simulation and system reaction network topology analysis. We hope that this work can provide insights to tackle the challenging problem of assessment of combinational drug therapy effect in a large scale signaling pathway. And hopefully in the future our method could be expanded to more general criteria.

Signalling complexes and clusters: functional advantages and methodological hurdles

Signalling molecules integrate, codify and transport information in cells. Organisation of these molecules in complexes and clusters improves the efficiency, fidelity and robustness of cellular signalling. Here, we summarise current views on how signalling molecules assemble into macromolecular complexes and clusters and how they use their physical properties to transduce environmental information into a variety of cellular processes. In addition, we discuss recent innovations in live-cell imaging at the sub-micrometer scale and the challenges of object (particle) tracking, both of which help us to observe signalling complexes and clusters and to examine their dynamic character.

A comprehensive molecular interaction map for rheumatoid arthritis

Background

Computational biology contributes to a variety of areas related to life sciences and, due to the growing impact of translational medicine - the scientific approach to medicine in tight relation with basic science -, it is becoming an important player in clinical-related areas. In this study, we use computation methods in order to improve our understanding of the complex interactions that occur between molecules related to Rheumatoid Arthritis (RA).

Methodology

Due to the complexity of the disease and the numerous molecular players involved, we devised a method to construct a systemic network of interactions of the processes ongoing in patients affected by RA. The network is based on high-throughput data, refined semi-automatically with carefully curated literature-based information. This global network has then been topologically analysed, as a whole and tissue-specifically, in order to translate the experimental molecular connections into topological motifs meaningful in the identification of tissue-specific markers and targets in the diagnosis, and possibly in the therapy, of RA.

Significance

We find that some nodes in the network that prove to be topologically important, in particular AKT2, IL6, MAPK1 and TP53, are also known to be associated with drugs used for the treatment of RA. Importantly, based on topological consideration, we are also able to suggest CRKL as a novel potentially relevant molecule for the diagnosis or treatment of RA. This type of finding proves the potential of in silico analyses able to produce highly refined hypotheses, based on vast experimental data, to be tested further and more efficiently. As research on RA is ongoing, the present map is in fieri, despite being -at the moment- a reflection of the state of the art. For this reason we make the network freely available in the standardised and easily exportable .xml CellDesigner format at ‘www.picb.ac.cn/ClinicalGenomicNTW/temp.html’ and ‘www.celldesigner.org’.

13 Networks II: Teamwork

This chapter shows that for many tasks the use of signals is crucial in establishing the coordination needed for effective teamwork. Teamwork may in some circumstances be achieved by a simple exchange of signals between equals. In other situations a good team may need a leader.

3 Information

This chapter shows that information is carried by signals. It flows through signaling networks that not only transmit it, but also filter, combine, and process it in various ways. We can investigate the flow of information using a framework of generalized signaling games. The dynamics of evolution and learning in these games illuminate the creation and flow of information.

7 Learning

This chapter argues that investigation of reinforcement learning is a complement to the study of belief learning, rather than being a ‘dangerous antagonist’. It begins at the low end of the scale, to see how far simple reinforcement learning can get us, and then move up. Exactly how does degree of reinforcement affect the strengthening of the bond between stimulus and response? Different answers are possible, and these yield alternative theories of the law of effect.

11 Networks I: Logic and Information Processing

This chapter discusses the combination of simple signals to form complex signals. When multiple senders convey different information to a receiver (or to multiple receivers) the receiver is confronted with a problem of information processing. How does one take all these inputs and fix on what to output — what to do? Logical inference is only part of this bigger problem of information processing. It is a problem routinely solved every second by our nervous system as floods of sensory information are filtered, integrated, and used to control conscious and unconscious actions.

12 Complex Signals and Compositionality

This chapter focuses on an earlier point in the evolution of signaling. It considers how one might come to have — in the most primitive way — a complex signal composed of simple signals. This is done with the smallest departure possible from signaling models that have been previously examined in this book.

5 Evolution in Lewis Signaling Games

Signaling systems had been shown to be the only evolutionarily stable strategies in n-state, n-signal, and n-act signaling games. They were the only attractors in the replicator dynamics. In simple cases, it was clear why almost every possible starting point was carried to a signaling system. This chapter considers how far these positive results generalize.

2 Signals in Nature

This chapter surveys some of the signaling systems in nature. Darwin sees some kind of natural salience operating at the origin of language. At that point signals are not conventional, but rather the signal is somehow naturally suited to convey its content. Signaling is then gradually modified by evolution.

10 Inventing New Signals

This chapter presents a simple, tractable model for the invention of new signals. It can be easily studied by simulation, and connections with well-studied processes from population genetics suggest that analytic results are not completely out of reach.

6 Deception

This chapter shows that in all kinds of signaling systems in nature there is information transmission which is sufficient to maintain signaling, but there is also misinformation and even deception. Misinformation is straightforward. If receipt of a signal moves probabilities of states it contains information about the state. If it moves the probability of a state in the wrong direction — either by diminishing the probability of the state in which it is sent, or raising the probability of a state other than the one in which it is sent — then it is misleading information, or misinformation. If misinformation is sent systematically and benefits the sender at the expense of the receiver, then it is deception.

8 Learning in Lewis Signaling Games

This chapter argues that we can and do learn to signal. We are not the only species able to do this, although others may not do it so well. The real question is what is required to be able to learn to signal. Or, better, what kind of learning is capable of spontaneously generating signaling? If the learning somehow has the signaling system preprogramed in, then learning to signal is not very interesting. If the learning mechanism is general purpose and low level, learning to signal is quite interesting.

14 Learning to Network

This chapter introduces a low-rationality probe and adjust dynamics to approximate higher rationality learning in the basic Bala–Goyal models. Both best response dynamics and probe and adjust learned networks that reinforcement learning did not. In general, probe and adjust learns a network structure if best response with inertia does.

9 Generalizing Signaling Games: Synonyms, Bottlenecks, Category Formation

This chapter presents a model of signaling with invention of new signals. It maintains the assumption that in all contingencies sender and receiver get the same payoff. But even where sender and receiver continue to have pure common interest, relaxing the strict assumptions on payoffs imposed so far may lead to new phenomena.

1 Signals

Whatever one thinks of human signals, it must be acknowledged that information is transmitted by signaling systems at all levels of biological organization. Monkeys, birds, bees, and even bacteria have signaling systems. Multicellular organisms are only possible because internal signals coordinate the actions of their constituents. This chapter addresses two main questions: How can interacting individuals spontaneously learn to signal? How can species spontaneously evolve signalling systems? It discusses how we can bring contemporary theoretical tools to bear on these questions.