A systems- and signal-oriented approach to intracellular dynamics

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general theory of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A theory is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present theory makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the theory holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

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.

Open cascades as simple solutions to providing ultrasensitivity and adaptation in cellular signaling

Cell signaling is achieved predominantly by reversible phosphorylation-dephosphorylation reaction cascades. Up until now, circuits conferring adaptation have all required the presence of a cascade with some type of closed topology: negative-feedback loop with a buffering node, or incoherent feed-forward loop with a proportioner node. In this paper--using Goldbeter and Koshland-type expressions--we propose a differential equation model to describe a generic, open signaling cascade that elicits an adaptation response. This is accomplished by coupling N phosphorylation-dephosphorylation cycles unidirectionally, without any explicit feedback loops. Using this model, we show that as the length of the cascade grows, the steady states of the downstream cycles reach a limiting value. In other words, our model indicates that there are a minimum number of cycles required to achieve a maximum in sensitivity and amplitude in the response of a signaling cascade. We also describe for the first time that the phenomenon of ultrasensitivity can be further subdivided into three sub-regimes, separated by sharp stimulus threshold values: OFF, OFF-ON-OFF, and ON. In the OFF-ON-OFF regime, an interesting property emerges. In the presence of a basal amount of activity, the temporal evolution of early cycles yields damped peak responses. On the other hand, the downstream cycles switch rapidly to a higher activity state for an extended period of time, prior to settling to an OFF state (OFF-ON-OFF). This response arises from the changing dynamics between a feed-forward activation module and dephosphorylation reactions. In conclusion, our model gives the new perspective that open signaling cascades embedded in complex biochemical circuits may possess the ability to show a switch-like adaptation response, without the need for any explicit feedback circuitry.

Dynamic modeling and simulation of JNK and P38 kinase cascades with feedbacks and crosstalks

All cells receive and respond to signals from their environment, whether they live freely or are part of a tissue. Feedback loops are one among the interactions in signal-transduction cascades, in which the information from the downstream components is sent back to the upstream components of the system. Crosstalks between signal-transduction cascades are able to combine the information's received and processed to trigger the appropriate response. To understand how signaling networks make decisions, the dynamic interactions of proteins in the signal-transduction cascades are important rather than just creating static maps of pathways. Based on reaction kinetics, we have developed mathematical models to predict and analyze the impacts of the feedback loops in JNK cascades and the crosstalks between JNK and P38 kinase cascades. Feedback loops in JNK cascades and crosstalks between JNK and P38 kinase cascades plays the complementary roles in making the impacts on the activation of JNK and P38 kinases. JNK and P38 kinase cascades with feedbacks and crosstalks is a robust system.

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

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Goldbeter-Koshland model for open signaling cascades: a mathematical study

A modified Goldbeter-Koshland (GK) type model is proposed to study the open signaling cascade with forward activation. Three different regimes related to the ultrasensitivity are clearly defined. When the cascade is sufficiently long, the steady states in the downstream cycles exhibit a limiting behavior. Meanwhile, a temporal switch-like behavior is revealed in the pre-ultrasensitivity regime without any feedback circuitry. A detailed analysis of this phenomenon is provided.

The control of the controller: molecular mechanisms for robust perfect adaptation and temperature compensation

Organisms have the property to adapt to a changing environment and keep certain components within a cell regulated at the same level (homeostasis). "Perfect adaptation" describes an organism's response to an external stepwise perturbation by regulating some of its variables/components precisely to their original preperturbation values. Numerous examples of perfect adaptation/homeostasis have been found, as for example, in bacterial chemotaxis, photoreceptor responses, MAP kinase activities, or in metal-ion homeostasis. Two concepts have evolved to explain how perfect adaptation may be understood: In one approach (robust perfect adaptation), the adaptation is a network property, which is mostly, but not entirely, independent of rate constant values; in the other approach (nonrobust perfect adaptation), a fine-tuning of rate constant values is needed. Here we identify two classes of robust molecular homeostatic mechanisms, which compensate for environmental variations in a controlled variable's inflow or outflow fluxes, and allow for the presence of robust temperature compensation. These two classes of homeostatic mechanisms arise due to the fact that concentrations must have positive values. We show that the concept of integral control (or integral feedback), which leads to robust homeostasis, is associated with a control species that has to work under zero-order flux conditions and does not necessarily require the presence of a physico-chemical feedback structure. There are interesting links between the two identified classes of homeostatic mechanisms and molecular mechanisms found in mammalian iron and calcium homeostasis, indicating that homeostatic mechanisms may underlie similar molecular control structures.

Analysis of the impact of ERK5, JNK, and P38 kinase cascades on each other: a systems approach

The classical concept of linear pathways is being increasingly challenged by network representations, which emphasize the importance of interactions between components of a biological system, and motivates for adopting a system-level approach in biology. We have developed a dynamical system that integrates quantitative, dynamic and topological representation of network of ERK5 (Extracellular signal-regulated kinases 5), JNK(c-Jun N-terminal kinases) and P38 kinase cascades. We have observered that, the transient activation of ERK5, JNK1 and P38beta kinase, and the persistent activation of JNK2, JNK3 and P38 delta kinase does not get affected due to the cross-talks between ERK5, JNK and P38 kinase cascades. But it is due to the cross - talks, the transiently activated P38alpha kinase become inactivated, and the transiently activated P38gamma kinase become persistently activated. The impacts of one-way cross-talks between the cascades are insignificant and differ from the impact of two-way cross-talks. We generate a hypothesis that, signaling pathways should be studied as a system by considering the cross-talks between the two adjacent cascades.

Computational prediction and analysis of impact of the cross-talks between JNK and P38 kinase cascades

Signal transduction is a complex protein signaling process with a rich network of multifunctional interactions that occur in a non-linear fashion. Mitogen-activated protein kinase (MAPK) signal transduction pathways regulate diverse cellular processes ranging from proliferation and differentiation to apoptosis. In mammals, out of five, there are three well characterized subfamilies of MAPKs - ERKs (Extracellular signal-regulated kinases), JNKs (c-Jun N-terminal kinases), and P38 kinases, and their activators, are implicated in human diseases and are targets for drug development. Kinase cascades in MAPK pathways mediate the sensing and processing of stimuli. To understand how cells makes decisions, the dynamic interactions of components of signaling cascades are important rather than just creating static maps. Based on enzyme kinetic reactions, we have developed a mathematical model to analyze the impact of the cross-talks between JNK and P38 kinase cascades. Cross-talks between JNK and P38 kinase cascades influence the activities of P38 kinases. Responses of the signals should be studied for network of kinase cascades by considering cross-talks.

The role of dynamic stimulation pattern in the analysis of bistable intracellular networks

Bistable systems play an important role in the functioning of living cells. Depending on the strength of the necessary positive feedback one can distinguish between (irreversible) "one-way switch" or (reversible) "toggle-switch" type behavior. Besides the well- established steady-state properties, some important characteristics of bistable systems arise from an analysis of their dynamics. We demonstrate that a supercritical stimulus amplitude is not sufficient to move the system from the lower (off-state) to the higher branch (on-state) for either a step or a pulse input. A switching surface is identified for the system as a function of the initial condition, input pulse amplitude and duration (a supercritical signal). We introduce the concept of bounded autonomy for single level systems with a pulse input. Towards this end, we investigate and characterize the role of the duration of the stimulus. Furthermore we show, that a minimal signal power is also necessary to change the steady state of the bistable system. This limiting signal power is independent of the applied stimulus and is determined only by systems parameters. These results are relevant for the design of experiments, where it is often difficult to create a defined pattern for the stimulus. Furthermore, intracellular processes, like receptor internalization, do manipulate the level of stimulus such that level and duration of the stimulus is conducive to characteristic behavior.

A hidden feedback in signaling cascades is revealed

Cycles involving covalent modification of proteins are key components of the intracellular signaling machinery. Each cycle is comprised of two interconvertable forms of a particular protein. A classic signaling pathway is structured by a chain or cascade of basic cycle units in such a way that the activated protein in one cycle promotes the activation of the next protein in the chain, and so on. Starting from a mechanistic kinetic description and using a careful perturbation analysis, we have derived, to our knowledge for the first time, a consistent approximation of the chain with one variable per cycle. The model we derive is distinct from the one that has been in use in the literature for several years, which is a phenomenological extension of the Goldbeter-Koshland biochemical switch. Even though much has been done regarding the mathematical modeling of these systems, our contribution fills a gap between existing models and, in doing so, we have unveiled critical new properties of this type of signaling cascades. A key feature of our new model is that a negative feedback emerges naturally, exerted between each cycle and its predecessor. Due to this negative feedback, the system displays damped temporal oscillations under constant stimulation and, most important, propagates perturbations both forwards and backwards. This last attribute challenges the widespread notion of unidirectionality in signaling cascades. Concrete examples of applications to MAPK cascades are discussed. All these properties are shared by the complete mechanistic description and our simplified model, but not by previously derived phenomenological models of signaling cascades.

Proteins, drug targets and the mechanisms they control: the simple truth about complex networks

Realizing the promise of molecularly targeted inhibitors for cancer therapy will require a new level of knowledge about how a drug target is wired into the control circuitry of a complex cellular network. Here we review general homeostatic principles of cellular networks that enable the cell to be resilient in the face of molecular perturbations, while at the same time being sensitive to subtle input signals. Insights into such mechanisms may facilitate the development of combination therapies that take advantage of the cellular control circuitry, with the aim of achieving higher efficacy at a lower drug dosage and with a reduced probability of drug-resistance development.

A hidden oncogenic positive feedback loop caused by crosstalk between Wnt and ERK pathways

The Wnt and the extracellular signal regulated-kinase (ERK) pathways are both involved in the pathogenesis of various kinds of cancers. Recently, the existence of crosstalk between Wnt and ERK pathways was reported. Gathering all reported results, we have discovered a positive feedback loop embedded in the crosstalk between the Wnt and ERK pathways. We have developed a plausible model that represents the role of this hidden positive feedback loop in the Wnt/ERK pathway crosstalk based on the integration of experimental reports and employing established basic mathematical models of each pathway. Our analysis shows that the positive feedback loop can generate bistability in both the Wnt and ERK signaling pathways, and this prediction was further validated by experiments. In particular, using the commonly accepted assumption that mutations in signaling proteins contribute to cancerogenesis, we have found two conditions through which mutations could evoke an irreversible response leading to a sustained activation of both pathways. One condition is enhanced production of beta-catenin, the other is a reduction of the velocity of MAP kinase phosphatase(s). This enables that high activities of Wnt and ERK pathways are maintained even without a persistent extracellular signal. Thus, our study adds a novel aspect to the molecular mechanisms of carcinogenesis by showing that mutational changes in individual proteins can cause fundamental functional changes well beyond the pathway they function in by a positive feedback loop embedded in crosstalk. Thus, crosstalk between signaling pathways provides a vehicle through which mutations of individual components can affect properties of the system at a larger scale.

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior.

Cell-signalling dynamics in time and space

The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signalling networks. Temporal dynamics are coupled to spatial gradients of signalling activities, which guide pivotal intracellular processes and tightly regulate signal propagation across a cell. Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.