Mathematical models of specificity in cell signaling

Mathematical Modeling and Inference of Epidermal Growth Factor-Induced Mitogen-Activated Protein Kinase Cell Signaling Pathways

The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.

Comparisons of two receptor-MAPK pathways in a single cell-type reveal mechanisms of signalling specificity

Cells harbour numerous receptor pathways to respond to diverse stimuli, yet often share common downstream signalling components. Mitogen-activated protein kinase (MPK) cascades are an example of such common hubs in eukaryotes. How such common hubs faithfully transduce distinct signals within the same cell-type is insufficiently understood, yet of fundamental importance for signal integration and processing in plants. We engineered a unique genetic background allowing direct comparisons of a developmental and an immunity pathway in one cell-type, the Arabidopsis root endodermis. We demonstrate that the two pathways maintain distinct functional and transcriptional outputs despite common MPK activity patterns. Nevertheless, activation of different MPK kinases and MPK classes led to distinct functional readouts, matching observed pathway-specific readouts. On the basis of our comprehensive analysis of core MPK signalling elements, we propose that combinatorial activation within the MPK cascade determines the differential regulation of an endodermal master transcription factor, MYB36, that drives pathway-specific gene activation.

Atherosclerosis and Inflammation: Insights from the Theory of General Pathological Processes

Recent advances have greatly improved our understanding of the molecular mechanisms behind atherosclerosis pathogenesis. However, there is still a need to systematize this data from a general pathology perspective, particularly with regard to atherogenesis patterns in the context of both canonical and non-classical inflammation types. In this review, we analyze various typical phenomena and outcomes of cellular pro-inflammatory stress in atherosclerosis, as well as the role of endothelial dysfunction in local and systemic manifestations of low-grade inflammation. We also present the features of immune mechanisms in the development of productive inflammation in stable and unstable plaques, along with their similarities and differences compared to canonical inflammation. There are numerous factors that act as inducers of the inflammatory process in atherosclerosis, including vascular endothelium aging, metabolic dysfunctions, autoimmune, and in some cases, infectious damage factors. Life-critical complications of atherosclerosis, such as cardiogenic shock and severe strokes, are associated with the development of acute systemic hyperinflammation. Additionally, critical atherosclerotic ischemia of the lower extremities induces paracoagulation and the development of chronic systemic inflammation. Conversely, sepsis, other critical conditions, and severe systemic chronic diseases contribute to atherogenesis. In summary, atherosclerosis can be characterized as an independent form of inflammation, sharing similarities but also having fundamental differences from low-grade inflammation and various variants of canonical inflammation (classic vasculitis).

Inflammation: A New Look at an Old Problem

Pro-inflammatory stress is inherent in any cells that are subject to damage or threat of damage. It is defined by a number of universal components, including oxidative stress, cellular response to DNA damage, unfolded protein response to mitochondrial and endoplasmic reticulum stress, changes in autophagy, inflammasome formation, non-coding RNA response, formation of an inducible network of signaling pathways, and epigenetic changes. The presence of an inducible receptor and secretory phenotype in many cells is the cause of tissue pro-inflammatory stress. The key phenomenon determining the occurrence of a classical inflammatory focus is the microvascular inflammatory response (exudation, leukocyte migration to the alteration zone). This same reaction at the systemic level leads to the development of life-critical systemic inflammation. From this standpoint, we can characterize the common mechanisms of pathologies that differ in their clinical appearance. The division of inflammation into alternative variants has deep evolutionary roots. Evolutionary aspects of inflammation are also described in the review. The aim of the review is to provide theoretical arguments for the need for an up-to-date theory of the relationship between key human pathological processes based on the integrative role of the molecular mechanisms of cellular and tissue pro-inflammatory stress.

The Pathogenesis of End-Stage Renal Disease from the Standpoint of the Theory of General Pathological Processes of Inflammation

Chronic kidney disease can progress to end-stage chronic renal disease (ESRD), which requires the use of replacement therapy (dialysis or kidney transplant) in life-threatening conditions. In ESRD, irreversible changes in the kidneys are associated with systemic changes of proinflammatory nature and dysfunctions of internal organs, skeletal muscles, and integumentary tissues. The common components of ESRD pathogenesis, regardless of the initial nosology, are (1) local (in the kidneys) and systemic chronic low-grade inflammation (ChLGI) as a risk factor for diabetic kidney disease and its progression to ESRD, (2) inflammation of the classical type characteristic of primary and secondary autoimmune glomerulonephritis and infectious recurrent pyelonephritis, as well as immune reactions in kidney allograft rejection, and (3) chronic systemic inflammation (ChSI), pathogenetically characterized by latent microcirculatory disorders and manifestations of paracoagulation. The development of ChSI is closely associated with programmed hemodialysis in ESRD, as well as with the systemic autoimmune process. Consideration of ESRD pathogenesis from the standpoint of the theory of general pathological processes opens up the scope not only for particular but also for universal approaches to conducting pathogenetic therapies and diagnosing and predicting systemic complications in severe nephropathies.

Problems of Pathogenesis and Pathogenetic Therapy of COVID-19 from the Perspective of the General Theory of Pathological Systems (General Pathological Processes)

The COVID-19 pandemic examines not only the state of actual health care but also the state of fundamental medicine in various countries. Pro-inflammatory processes extend far beyond the classical concepts of inflammation. They manifest themselves in a variety of ways, beginning with extreme physiology, then allostasis at low-grade inflammation, and finally the shockogenic phenomenon of "inflammatory systemic microcirculation". The pathogenetic core of critical situations, including COVID-19, is this phenomenon. Microcirculatory abnormalities, on the other hand, lie at the heart of a specific type of general pathological process known as systemic inflammation (SI). Systemic inflammatory response, cytokine release, cytokine storm, and thrombo-inflammatory syndrome are all terms that refer to different aspects of SI. As a result, the metabolic syndrome model does not adequately reflect the pathophysiology of persistent low-grade systemic inflammation (ChSLGI). Diseases associated with ChSLGI, on the other hand, are risk factors for a severe COVID-19 course. The review examines the role of hypoxia, metabolic dysfunction, scavenger receptors, and pattern-recognition receptors, as well as the processes of the hemophagocytic syndrome, in the systemic alteration and development of SI in COVID-19.

Cellular Stress and General Pathological Processes

From the viewpoint of the general pathology, most of the human diseases are associated with a limited number of pathogenic processes such as inflammation, tumor growth, thrombosis, necrosis, fibrosis, atrophy, pathological hypertrophy, dysplasia and metaplasia. The phenomenon of chronic low-grade inflammation could be attributed to non-classical forms of inflammation, which include many neurodegenerative processes, pathological variants of insulin resistance, atherosclerosis, and other manifestations of the endothelial dysfunction. Individual and universal manifestations of cellular stress could be considered as a basic element of all these pathologies, which has both physiological and pathophysiological significance. The review examines the causes, main phenomena, developmental directions and outcomes of cellular stress using a phylogenetically conservative set of genes and their activation pathways, as well as tissue stress and its role in inflammatory and para-inflammatory processes. The main ways towards the realization of cellular stress and its functional blocks were outlined. The main stages of tissue stress and the classification of its typical manifestations, as well as its participation in the development of the classical and non-classical variants of the inflammatory process, were also described. The mechanisms of cellular and tissue stress are structured into the complex systems, which include networks that enable the exchange of information with multidirectional signaling pathways which together make these systems internally contradictory, and the result of their effects is often unpredictable. However, the possible solutions require new theoretical and methodological approaches, one of which includes the transition to integral criteria, which plausibly reflect the holistic image of these processes.

A theoretical study on the cross-talk of stress regulatory pathways in root cells

The plants developed more dedicated regulatory pathways than the animals did to response various environment stresses, since they could not run away. The cross-talk among the pathways generally introduce non-trivial regulatory behaviors, from which the plants may benefit. For better understanding the regulatory mechanism due to cross-talk, we study in this work two entangled stress regulatory pathways in root cells. A quantitative model of the regulatory network is constructed in the simplest fashion. An analytic parameter-free approach is then employed to analyse the response tendencies. It leads us to a simple constraint on the non-linear regulatory exponents. Under the constraint, a transition to the non-monotonic growth inhibition happens at finite concentration of ABA, due to which the plants could survive from cold/heat stress. The parameter-free tendency analysis would also be applied to further experiments, especially in the case of insufficient data for multi-parameter fitting.

A postsynaptic PI3K-cII dependent signaling controller for presynaptic homeostatic plasticity

Presynaptic homeostatic plasticity stabilizes information transfer at synaptic connections in organisms ranging from insect to human. By analogy with principles of engineering and control theory, the molecular implementation of PHP is thought to require postsynaptic signaling modules that encode homeostatic sensors, a set point, and a controller that regulates transsynaptic negative feedback. The molecular basis for these postsynaptic, homeostatic signaling elements remains unknown. Here, an electrophysiology-based screen of the Drosophila kinome and phosphatome defines a postsynaptic signaling platform that includes a required function for PI3K-cII, PI3K-cIII and the small GTPase Rab11 during the rapid and sustained expression of PHP. We present evidence that PI3K-cII localizes to Golgi-derived, clathrin-positive vesicles and is necessary to generate an endosomal pool of PI(3)P that recruits Rab11 to recycling endosomal membranes. A morphologically distinct subdivision of this platform concentrates postsynaptically where we propose it functions as a homeostatic controller for retrograde, trans-synaptic signaling.

Coupled feedback loops control the stimulus-dependent dynamics of the yeast transcription factor Msn2

Information about environmental stimuli often can be encoded by the dynamics of signaling molecules or transcription factors. In the yeast Saccharomyces cerevisiae, different types of stresses induce distinct nuclear translocation dynamics of the general stress-responsive transcription factor Msn2, but the underlying mechanisms remain unclear. Using deterministic and stochastic modeling, we reproduced in silico the different dynamic responses of Msn2 to glucose limitation and osmotic stress observed in vivo and found that a positive feedback loop on protein kinase A mediated by the AMP-activated protein kinase Snf1 is coupled with a negative feedback loop to generate the characteristic pulsatile dynamics of Msn2. The model predicted that the stimulus-specific positive feedback loop could be responsible for the difference between Msn2 dynamics induced by glucose limitation and osmotic stress. This prediction was further verified experimentally by time-lapse microscopic examinations of the snf1Δ strain. In this mutant lacking the Snf1-mediated positive feedback loop, Msn2 responds similarly to glucose limitation and osmotic stress, and its pulsatile translocation is largely abrogated. Our combined computational and experimental analysis reveals a regulatory mechanism by which cells can encode information about environmental cues into distinct signaling dynamics through stimulus-specific network architectures.

Combined genomic and structural analyses of a cultured magnetotactic bacterium reveals its niche adaptation to a dynamic environment

BACKGROUND

Magnetotactic bacteria (MTB) are a unique group of prokaryotes that have a potentially high impact on global geochemical cycling of significant primary elements because of their metabolic plasticity and the ability to biomineralize iron-rich magnetic particles called magnetosomes. Understanding the genetic composition of the few cultivated MTB along with the unique morphological features of this group of bacteria may provide an important framework for discerning their potential biogeochemical roles in natural environments.

RESULTS

Genomic and ultrastructural analyses were combined to characterize the cultivated magnetotactic coccus Magnetofaba australis strain IT-1. Cells of this species synthesize a single chain of elongated, cuboctahedral magnetite (Fe₃O₄) magnetosomes that cause them to align along magnetic field lines while they swim being propelled by two bundles of flagella at velocities up to 300 μm s^-1. High-speed microscopy imaging showed the cells move in a straight line rather than in the helical trajectory described for other magnetotactic cocci. Specific genes within the genome of Mf. australis strain IT-1 suggest the strain is capable of nitrogen fixation, sulfur reduction and oxidation, synthesis of intracellular polyphosphate granules and transporting iron with low and high affinity. Mf. australis strain IT-1 and Magnetococcus marinus strain MC-1 are closely related phylogenetically although similarity values between their homologous proteins are not very high.

CONCLUSION

Mf. australis strain IT-1 inhabits a constantly changing environment and its complete genome sequence reveals a great metabolic plasticity to deal with these changes. Aside from its chemoautotrophic and chemoheterotrophic metabolism, genomic data indicate the cells are capable of nitrogen fixation, possess high and low affinity iron transporters, and might be capable of reducing and oxidizing a number of sulfur compounds. The relatively large number of genes encoding transporters as well as chemotaxis receptors in the genome of Mf. australis strain IT-1 combined with its rapid swimming velocities, indicate that cells respond rapidly to environmental changes.

Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

Barcode Sequencing Screen Identifies SUB1 as a Regulator of Yeast Pheromone Inducible Genes

The yeast pheromone response pathway serves as a valuable model of eukaryotic mitogen-activated protein kinase (MAPK) pathways, and transcription of their downstream targets. Here, we describe application of a screening method combining two technologies: fluorescence-activated cell sorting (FACS), and barcode analysis by sequencing (Bar-Seq). Using this screening method, and pFUS1-GFP as a reporter for MAPK pathway activation, we readily identified mutants in known mating pathway components. In this study, we also include a comprehensive analysis of the FUS1 induction properties of known mating pathway mutants by flow cytometry, featuring single cell analysis of each mutant population. We also characterized a new source of false positives resulting from the design of this screen. Additionally, we identified a deletion mutant, sub1Δ, with increased basal expression of pFUS1-GFP. Here, in the first ChIP-Seq of Sub1, our data shows that Sub1 binds to the promoters of about half the genes in the genome (tripling the 991 loci previously reported), including the promoters of several pheromone-inducible genes, some of which show an increase upon pheromone induction. Here, we also present the first RNA-Seq of a sub1Δ mutant; the majority of genes have no change in RNA, but, of the small subset that do, most show decreased expression, consistent with biochemical studies implicating Sub1 as a positive transcriptional regulator. The RNA-Seq data also show that certain pheromone-inducible genes are induced less in the sub1Δ mutant relative to the wild type, supporting a role for Sub1 in regulation of mating pathway genes. The sub1Δ mutant has increased basal levels of a small subset of other genes besides FUS1, including IMD2 and FIG1, a gene encoding an integral membrane protein necessary for efficient mating.

Crosstalk between pathways enhances the controllability of signalling networks

The control of complex networks is one of the most challenging problems in the fields of biology and engineering. In this study, the authors explored the controllability and control energy of several signalling networks, which consisted of many interconnected pathways, including networks with a bow-tie architecture. On the basis of the theory of structure controllability, they revealed that biological mechanisms, such as cross-pathway interactions, compartmentalisation and so on make the networks easier to fully control. Furthermore, using numerical simulations for two realistic examples, they demonstrated that the control energy of normal networks with crosstalk is lower than in networks without crosstalk. These results indicate that the biological networks are optimally designed to achieve their normal functions from the viewpoint of the control theory. The authors' work provides a comprehensive understanding of the impact of network structures and properties on controllability.

Paradoxical results in perturbation-based signaling network reconstruction

Mathematical models are extensively employed to understand physicochemical processes in biological systems. In the absence of detailed mechanistic knowledge, models are often based on network inference methods, which in turn rely upon perturbations to nodes by biochemical means. We have discovered a potential pitfall of the approach underpinning such methods when applied to signaling networks. We first show experimentally, and then explain mathematically, how even in the simplest signaling systems, perturbation methods may lead to paradoxical conclusions: for any given pair of two components X and Y, and depending upon the specific intervention on Y, either an activation or a repression of X could be inferred. This effect is of a different nature from incomplete network identification due to underdetermined data and is a phenomenon intrinsic to perturbations. Our experiments are performed in an in vitro minimal system, thus isolating the effect and showing that it cannot be explained by feedbacks due to unknown intermediates. Moreover, our in vitro system utilizes proteins from a pathway in mammalian (and other eukaryotic) cells that play a central role in proliferation, gene expression, differentiation, mitosis, cell survival, and apoptosis. This pathway is the perturbation target of contemporary therapies for various types of cancers. The results presented here show that the simplistic view of intracellular signaling networks being made up of activation and repression links is seriously misleading, and call for a fundamental rethinking of signaling network analysis and inference methods.

A technique for determining the signs of sensitivities of steady states in chemical reaction networks

This paper studies the direction of change of steady states to parameter perturbations in chemical reaction networks, and, in particular, to changes in conserved quantities. Theoretical considerations lead to the formulation of a computational procedure that provides a set of possible signs of such sensitivities. The procedure is purely algebraic and combinatorial, only using information on stoichiometry, and is independent of the values of kinetic constants. Three examples of important intracellular signal transduction models are worked out as an illustration. In these examples, the set of signs found is minimal, but there is no general guarantee that the set found will always be minimal in other examples. The paper also briefly discusses the relationship of the sign problem to the question of uniqueness of steady states in stoichiometry classes.

Multiplexing oscillatory biochemical signals

In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

Tunable signal processing through a kinase control cycle: the IKK signaling node

The transcription factor NFκB, a key component of the immune system, shows intricate stimulus-specific temporal dynamics. Those dynamics are thought to play a role in controlling the physiological response to cytokines and pathogens. Biochemical evidence suggests that the NFκB inducing kinase, IKK, a signaling hub onto which many signaling pathways converge, is regulated via a regulatory cycle comprising a poised, an active, and an inactive state. We hypothesize that it operates as a modulator of signal dynamics, actively reshaping the signals generated at the receptor proximal level. Here we show that a regulatory cycle can function in at least three dynamical regimes, tunable by regulating a single kinetic parameter. In particular, the simplest three-state regulatory cycle can generate signals with two well-defined phases, each with distinct coding capabilities in terms of the information they can carry about the stimulus. We also demonstrate that such a kinase cycle can function as a signal categorizer classifying diverse incoming signals into outputs with a limited set of temporal activity profiles. Finally, we discuss the extension of the results to other regulatory motifs that could be understood in terms of the regimes of the three-state cycle.

Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms

Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause–effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.

Identification of the molecular mechanisms for cell-fate selection in budding yeast through mathematical modeling

The specification and maintenance of cell fates is essential to the development of multicellular organisms. However, the precise molecular mechanisms in cell fate selection are, to our knowledge, poorly understood due to the complexity of multiple interconnected pathways. In this study, model-based quantitative analysis is used to explore how to maintain distinguished cell fates between cell-cycle commitment and mating arrest in budding yeast. We develop a full mathematical model of an interlinked regulatory network based on the available experimental data. By theoretically defining the Start transition point, the model is able to reproduce many experimental observations of the dynamical behaviors in wild-type cells as well as in Ste5-8A and Far1-S87A mutants. Furthermore, we demonstrate that a moderate ratio between Cln1/2→Far1 inhibition and Cln1/2→Ste5 inhibition is required to ensure a successful switch between different cell fates. We also show that the different ratios of the mutual Cln1/2 and Far1 inhibition determine the different cell fates. In addition, based on a new, definition of network entropy, we find that the Start point in wild-type cells coincides with the system's point of maximum entropy. This result indicates that Start is a transition point in the network entropy. Therefore, we theoretically explain the Start point from a network dynamics standpoint. Moreover, we analyze the biological bistablity of our model through bifurcation analysis. We find that the Cln1/2 and Cln3 production rates and the nonlinearity of SBF regulation on Cln1/2 production are potential determinants for irreversible entry into a new cell fate. Finally, the quantitative computations further reveal that high specificity and fidelity of the cell-cycle and mating pathways can guarantee specific cell-fate selection. These findings show that quantitative analysis and simulations with a mathematical model are useful tools for understanding the molecular mechanisms in cell-fate decisions.

The energy costs of insulators in biochemical networks

Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of modules--semiindependent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic futile cycles that consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a possible new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular plug-and-play interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.

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.

Protein scaffolds can enhance the bistability of multisite phosphorylation systems

The phosphorylation of a substrate at multiple sites is a common protein modification that can give rise to important structural and electrostatic changes. Scaffold proteins can enhance protein phosphorylation by facilitating an interaction between a protein kinase enzyme and its target substrate. In this work we consider a simple mathematical model of a scaffold protein and show that under specific conditions, the presence of the scaffold can substantially raise the likelihood that the resulting system will exhibit bistable behavior. This phenomenon is especially pronounced when the enzymatic reactions have sufficiently large K(M), compared to the concentration of the target substrate. We also find for a closely related model that bistable systems tend to have a specific kinetic conformation. Using deficiency theory and other methods, we provide a number of necessary conditions for bistability, such as the presence of multiple phosphorylation sites and the dependence of the scaffold binding/unbinding rates on the number of phosphorylated sites.

NOISE-INDUCED ALTERNATIVE RESPONSE IN MAP KINASE PATHWAYS WITH MUTUAL INHIBITION

All organisms have the ability to detect and respond to changes in the environment for survival, and as a result, specific cellular signaling pathways have evolved by which organisms sense their environment and respond to signals that they detect. However, an important unsolved problem in cell biology is to understand how specificity from signal to cellular response is maintained between different signal transduction pathways that share similar or identical components. Here, we show, using mathematical and computational modeling, that two typical signaling pathways in a single cell, hyperosmolar and pheromone motigen-avtivated protein kinase in the yeast Saccharomyces cerevisiae with mutual inhibition, can respond alternatively to two costimulated signals in a stochastically fluctuated environment. Within a bistable region over two input signals, noise plays an essential role in achieving specificity of response, while outside it, these pathways achieve specificity by filtering out spurious crosstalk through mutual inhibition.

Information theory based approaches to cellular signaling

BACKGROUND

Cells interact with their environment and they have to react adequately to internal and external changes such changes in nutrient composition, physical properties like temperature or osmolarity and other stresses. More specifically, they must be able to evaluate whether the external change is significant or just in the range of noise. Based on multiple external parameters they have to compute an optimal response. Cellular signaling pathways are considered as the major means of information perception and transmission in cells.

SCOPE OF REVIEW

Here, we review different attempts to quantify information processing on the level of individual cells. We refer to Shannon entropy, mutual information, and informal measures of signaling pathway cross-talk and specificity.

MAJOR CONCLUSIONS

Information theory in systems biology has been successfully applied to identification of optimal pathway structures, mutual information and entropy as system response in sensitivity analysis, and quantification of input and output information.

GENERAL SIGNIFICANCE

While the study of information transmission within the framework of information theory in technical systems is an advanced field with high impact in engineering and telecommunication, its application to biological objects and processes is still restricted to specific fields such as neuroscience, structural and molecular biology. However, in systems biology dealing with a holistic understanding of biochemical systems and cellular signaling only recently a number of examples for the application of information theory have emerged. This article is part of a Special Issue entitled Systems Biology of Microorganisms.

Multiplexing biochemical signals

In this Letter we show that living cells can multiplex biochemical signals, i.e., transmit multiple signals through the same signaling pathway simultaneously, and yet respond to them very specifically. We demonstrate how two binary input signals can be encoded in the concentration of a common signaling protein, which is then decoded such that each of the two output signals provides reliable information about one corresponding input. Under biologically relevant conditions the network can reach the maximum amount of information that can be transmitted, which is 2 bits.

The coupling of pathways and processes through shared components

Background

The coupling of pathways and processes through shared components is being increasingly recognised as a common theme which occurs in many cell signalling contexts, in which it plays highly non-trivial roles.

Results

In this paper we develop a basic modelling and systems framework in a general setting for understanding the coupling of processes and pathways through shared components. Our modelling framework starts with the interaction of two components with a common third component and includes production and degradation of all these components. We analyze the signal processing in our model to elucidate different aspects of the coupling. We show how different kinds of responses, including "ultrasensitive" and adaptive responses, may occur in this setting. We then build on the basic model structure and examine the effects of additional control regulation, switch-like signal processing, and spatial signalling. In the process, we identify a way in which allosteric regulation may contribute to signalling specificity, and how competitive effects may allow an enzyme to robustly coordinate and time the activation of parallel pathways.

Conclusions

We have developed and analyzed a common systems platform for examining the effects of coupling of processes through shared components. This can be the basis for subsequent expansion and understanding the many biologically observed variations on this common theme.

Design principles and specificity in biological networks with cross activation

Cells sense and respond to diverse environmental stimuli using a set of intracellular signaling components. Often, the signal transduction pathways contain shared components which lead to cross activation at different levels of the pathway. To discover the design principles that ensure signaling specificity is a challenging task, especially for pathways that contain numerous components. Here, we present an analysis of cross-activating pathways and show that a general inhibitory scheme, asymmetric hierarchical inhibition, is sufficient to ensure signaling specificity. Based on this inhibitory scheme, we are able to enumerate all possible network topologies containing two inhibitory links that guarantee specificity. Furthermore, we apply our methodology to the mating and filamentous growth pathways of the yeast model system Saccharomyces cerevisiae. We enumerate the possible ways to wire this model system and determine which topology is consistent with experimental data.

Modelling and experimental analysis of hormonal crosstalk in Arabidopsis

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. We have developed the first hormonal crosstalk network in Arabidopsis by iteratively combining modelling with experimental analysis.

We have revealed that the POLARIS gene interacts with the ethylene receptor and regulates both auxin transport and biosynthesis.

Our modelling analysis has reproduced all known mutants. With new experimental data, it has provided new insights into how the POLARIS gene regulates auxin concentration for root development in Arabidopsis, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling.

Modelling and experimental analysis have revealed that a bell-shaped dose–response relationship between endogenous auxin and root length is established via POLARIS.

Hormone signalling systems coordinate plant growth and development through a range of complex interactions. The activities of plant hormones, such as auxin, ethylene and cytokinin, depend on cellular context and exhibit interactions that can be either synergistic or antagonistic. An important question regarding the understanding of those interactions is how genes act on the crosstalk between hormones to regulate plant growth.

Previously, we identified the POLARIS (PLS) gene of Arabidopsis, which transcribes a short mRNA encoding a 36-amino acid peptide that is required for correct root growth and vascular development (Casson et al, 2002). Experimental evidence shows that there is a link between PLS, ethylene signalling, auxin homeostasis and microtubule cytoskeleton dynamics (Chilley et al, 2006). Specifically, mutation of PLS results in an enhanced ethylene-response phenotype, defective auxin transport and homeostasis, and altered sensitivity to microtubule inhibitors. These defects, along with the short-root phenotype, are suppressed by genetic and pharmacological inhibition of ethylene action. The expression of PLS is itself repressed by ethylene and induced by auxin. It was also shown that pls mutant roots are hyper-responsive to exogenous cytokinins and show increased expression of the cytokinin inducible gene ARR5/IBC6 compared with the wild type (Casson et al, 2002). Therefore, PLS may also be required for correct auxin–cytokinin homeostasis to modulate root growth.

In this study, we model PLS gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis.

Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport (Figures 1 and 4).

The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose–response relationship between endogenous auxin and root length is established via PLS.

In summary, we developed the first hormonal crosstalk model in Arabidopsis and revealed a hormonal crosstalk circuit through PLS and the downstream of ethylene signalling. Our study provides a platform to further integrate hormonal crosstalk in space and time in Arabidopsis.

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. In this study, we model POLARIS (PLS) gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis. Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport. The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose–response relationship between endogenous auxin and root length is established via PLS. This combined modelling and experimental analysis provides new insights into the integration of hormonal signals in plants.

Ultrasensitive responses and specificity in cell signaling

Background

Interconnected cell signaling pathways are able to efficiently and accurately transmit a multitude of different signals, despite an inherent potential for undesirable levels of cross-talk. To ensure that an appropriate response is produced, biological systems have evolved network-level mechanisms that insulate pathways from crosstalk and prevent 'leaking' or 'spillover' between pathways. Many signaling pathways have been shown to respond in an ultrasensitive (switch-like) fashion to graded input, and this behavior may influence specificity. The relationship of ultrasensitivity to signaling specificity has not been extensively explored.

Results

We studied the behavior of simple mathematical models of signaling networks composed of two interconnected pathways that share an intermediate component, asking if the two pathways in the network could exhibit both output specificity (preferentially activate their own output) and input fidelity (preferentially respond to their own input). Previous results with weakly-activated pathways indicated that neither mutual specificity nor mutual fidelity were obtainable in the absence of an insulating mechanism, such as cross-pathway inhibition, combinatorial signaling or scaffolding/compartmentalization. Here we found that mutual specificity is obtainable for hyperbolic or ultrasensitive pathways, even in the absence of an insulating mechanism. However, mutual fidelity is impossible at steady-state, even if pathways are hyperbolic or ultrasensitive. Nevertheless, ultrasensitivity does provide advantages in attaining specificity and fidelity to networks that contain an insulating mechanism. For networks featuring cross-pathway inhibition or combinatorial signaling, ultrasensitive activation can increase specificity in a limited way, and can only be utilized by one of the two pathways. In contrast, for networks featuring scaffolding/compartmentalization, ultrasensitive activation of both pathways can dramatically improve network specificity.

Conclusions

There are constraints to obtaining performance objectives associated with signaling specificity; such constraints may have influenced the evolution of signal transduction networks. Notably, input fidelity (preferential response to an authentic input) is a more difficult objective to achieve than output specificity (preferential targeting to an authentic output). Indeed, mutual fidelity is impossible in the absence of an insulating mechanism, even if pathways are ultrasensitive. Ultrasensitivity does, however, significantly enhance the performance of several insulating mechanisms. In particular, the ultrasensitive activation of both pathways can provide substantial improvement to networks containing scaffolding/compartmentalization.

Signal response sensitivity in the yeast mitogen-activated protein kinase cascade

The yeast pheromone response pathway is a canonical three-step mitogen activated protein kinase (MAPK) cascade which requires a scaffold protein for proper signal transduction. Recent experimental studies into the role the scaffold plays in modulating the character of the transduced signal, show that the presence of the scaffold increases the biphasic nature of the signal response. This runs contrary to prior theoretical investigations into how scaffolds function. We describe a mathematical model of the yeast MAPK cascade specifically designed to capture the experimental conditions and results of these empirical studies. We demonstrate how the system can exhibit either graded or ultrasensitive (biphasic) response dynamics based on the binding kinetics of enzymes to the scaffold. At the basis of our theory is an analytical result that weak interactions make the response biphasic while tight interactions lead to a graded response. We then show via an analysis of the kinetic binding rate constants how the results of experimental manipulations, modeled as changes to certain of these binding constants, lead to predictions of pathway output consistent with experimental observations. We demonstrate how the results of these experimental manipulations are consistent within the framework of our theoretical treatment of this scaffold-dependent MAPK cascades, and how future efforts in this style of systems biology can be used to interpret the results of other signal transduction observations.

Mechanisms and constraints on yeast MAPK signaling specificity

The survival of cells relies on their ability to respond specifically to diverse environmental signals. Surprisingly, intracellular signaling pathways often share the same or homologous protein components, yet undesirable crosstalk is, in general, suppressed. This signaling specificity has been well studied in the yeast model system Saccharomyces cerevisiae, where the mitogen-activated protein kinase (MAPK) cascades are repeatedly employed in mediating distinct biological processes including pheromone-induced mating and filamentous growth under starvation. Although various mechanisms have been proposed to interpret the yeast MAPK signaling specificity, a consistent theory is still lacking. Here, we present a mathematical model that shows signaling specificity can arise through asymmetric hierarchical inhibition. The parameters of our model are, where possible, based on experimental data that allow us to determine the constraints imposed by signaling specificity on these parameters. Our model is in broad agreement with experimental observations to date and generates testable predictions that may stimulate further research.

Cascading signaling pathways improve the fidelity of a stochastically and deterministically simulated molecular RS latch

Background

While biological systems have often been compared with digital systems, they differ by the strong effect of crosstalk between signals due to diffusivity in the medium, reaction kinetics and geometry. Memory elements have allowed the creation of autonomous digital systems and although biological systems have similar properties of autonomy, equivalent memory mechanisms remain elusive. Any such equivalent memory system, however, must silence the effect of crosstalk to maintain memory fidelity.

Results

Here, we present a system of enzymatic reactions that behaves like an RS latch (a simple memory element in digital systems). Using both a stochastic molecular simulator and ordinary differential equation simulator, we showed that crosstalk between two latches operating in the same spatial localization disrupts the memory fidelity of both latches. Crosstalk was reduced or silenced when simple reaction loops were replaced with multiple step or cascading reactions, showing that cascading signaling pathways are less susceptible to crosstalk.

Conclusion

Thus, the common biological theme of cascading signaling pathways is advantageous for maintaining the fidelity of a memory latch in the presence of crosstalk. The experimental implementation of such a latch system will lead to novel approaches to cell control using synthetic proteins and will contribute to our understanding of why cells behave differently even when given the same stimulus.

Specificity and robustness of the mammalian MAPK-IEG network

The mitogen-activated protein kinase cascade is a conserved signal transduction pathway found in organisms of complexity spanning from yeast to humans. In many mammalian tissue types, this pathway can correctly transduce signals from different extracellular messengers, leading to specific and often mutually exclusive cellular responses. The transduced signal is tuned by a complicated set of positive and negative feedback control mechanisms and fed into a downstream gene expression network. This network, based on the immediate early gene system, has two possible, mutually exclusive outcomes. Using a mathematical model, we study how different stimuli lead to different temporal signal structure. Further, we investigate how each of the feedback controls contributes to the overall specificity of the gene expression output, and hypothesize that the complicated nature of the mammalian mitogen-activated protein kinase pathway results in a system able to robustly identify and transduce the proper signal without investing in two completely separate signal cascades. Finally, we quantify the role of the RKIP protein in shaping the signal, and propose a novel mechanism of its involvement in cancer metastasis.

A post-translational modification code for transcription factors: sorting through a sea of signals

Cellular responses to environmental or physiological cues rely on transduction pathways that must ensure discrimination between different signals. These cascades 'crosstalk' and lead to a combinatorial regulation. This often results in different combinations of post-translational modifications (PTMs) on target proteins, which might act as a molecular barcode. Although appealing, the idea of the existence of such a code for transcription factors is debated. Using general arguments and recent evidence, we propose that a PTM code is not only possible but necessary in the context of transcription factors regulating multiple processes. Thus, the coding potential of PTM combinations should both provide a further layer of information integration from several transduction pathways and warrant highly specific cellular outputs.

Cross-regulatory mechanisms in hormone signaling

Recent studies suggest that hormones act through a web of interacting responses rather than through isolated linear pathways. This signal integration architecture may be one mechanism for increasing the specificity of outcomes in different cellular contexts. Several common themes for cross-regulation between pathways can be observed. Here, we propose a classification scheme for different levels of signaling pathway cross-regulation. This scheme is based on which parts of the individual pathways are acting as information conduits between pathways. Examples from the recent plant hormone biology literature are used to illustrate the different modes of interaction.

Signal duration and the time scale dependence of signal integration in biochemical pathways

Background

Signal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.

Results

Here we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.

Conclusion

We show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.

Signal integration in bacterial two-component regulatory systems

Two-component systems (TCSs) and phosphorelays are key mediators of bacterial signal transduction. The signals activating these systems promote the phosphorylated state of a response regulator, which is generally the form that carries out specific functions such as binding to DNA and catalysis of biochemical reactions. An emerging class of proteins-termed TCS connectors-modulate the output of TCSs by affecting the phosphorylation state of response regulators. TCS connectors use different mechanisms of action for signal integration, as well as in the coordination and fine-tuning of cellular processes. Present in both Gram-positive and Gram-negative bacteria, TCS connectors are critical for a variety of physiological functions including sporulation, competence, antibiotic resistance, and the transition to stationary phase.

Fus3-triggered Tec1 degradation modulates mating transcriptional output during the pheromone response

The yeast transcription factor Ste12 controls both mating and filamentation pathways. Upon pheromone induction, the mitogen-activated protein kinases, Fus3 and Kss1, activate Ste12 by relieving the repression of two functionally redundant Ste12 inhibitors, Dig1 and Dig2. Mating genes are controlled by the Ste12/Dig1/Dig2 complex through Ste12-binding sites, whereas filamentation genes are regulated by the Tec1/Ste12/Dig1 complex through Tec1-binding sites. The two Ste12 complexes are mutually exclusive. During pheromone response, Tec1 is degraded upon phosphorylation by Fus3, preventing cross-activation of the filamentation pathway. Here, we show that a stable Tec1 also impairs the induction of mating genes. A mathematical model is developed to capture the dynamic formation of the two Ste12 complexes and their interactions with pathway-specific promoters. By model simulations and experimentation, we show that excess Tec1 can impair the mating transcriptional output because of its ability to sequester Ste12, and because of a novel function of Dig2 for the transcription of mating genes. We suggest that Fus3-triggered Tec1 degradation is an important part of the transcriptional induction of mating genes during the pheromone response.

Uncovering signal transduction networks from high-throughput data by integer linear programming

Signal transduction is an important process that transmits signals from the outside of a cell to the inside to mediate sophisticated biological responses. Effective computational models to unravel such a process by taking advantage of high-throughput genomic and proteomic data are needed to understand the essential mechanisms underlying the signaling pathways. In this article, we propose a novel method for uncovering signal transduction networks (STNs) by integrating protein interaction with gene expression data. Specifically, we formulate STN identification problem as an integer linear programming (ILP) model, which can be actually solved by a relaxed linear programming algorithm and is flexible for handling various prior information without any restriction on the network structures. The numerical results on yeast MAPK signaling pathways demonstrate that the proposed ILP model is able to uncover STNs or pathways in an efficient and accurate manner. In particular, the prediction results are found to be in high agreement with current biological knowledge and available information in literature. In addition, the proposed model is simple to be interpreted and easy to be implemented even for a large-scale system.

Mapping dynamic protein interactions in MAP kinase signaling using live-cell fluorescence fluctuation spectroscopy and imaging

Fluorescence correlation spectroscopy (FCS), fluorescence cross-correlation spectroscopy (FCCS), and photon counting histograms (PCH) are fluctuation methods that emerged recently as potentially useful tools for obtaining parameters of molecular dynamics, interactions, and oligomerization in vivo. Here, we report the successful implementation of FCS, FCCS, and PCH in live yeast cells using fluorescent protein-tagged proteins expressed from their native chromosomal loci, examining cytosolic dynamics and interactions among components of the mitogen activated protein kinase (MAPK) cascade, a widely occurring signaling motif, in response to mating pheromone. FCS analysis detailed the diffusion characteristics and mobile concentrations of MAPK proteins. FCCS analysis using EGFP and mCherry-tagged protein pairs observed the interactions of Ste7 (MAPK kinase) with the MAPKs, Fus3 or Kss1, and of the scaffold protein, Ste5, with Ste7 and Ste11 (MAPK kinase kinase) in the cytosol, providing in vivo constants of their binding equilibrium. The interaction of Ste5 with Fus3 in the cytosol was below the limit of detection, suggesting a weak interaction, if it exists, with K(d) >400-500 nM. Using PCH, we show that cytosolic Ste5 were mostly monomers. Artificial dimerization of Ste5, as confirmed by PCH, using a dimerizing tag, stimulated the interaction between Ste5 and Fus3. Native Ste5 was found to bind Fus3 preferentially at the cortex in pheromone-treated cells, as detected by fluorescence resonance energy transfer (FRET). These results provide a quantitative spatial map of MAPK complexes in vivo and directly support the model that membrane association and regulation of the Ste5 scaffold are critical steps in MAPK activation.

Membrane recruitment of scaffold proteins drives specific signaling

Cells must give the right response to each stimulus they receive. Scaffolding, a signaling process mediated by scaffold proteins, participates in the decoding of the cues by specifically directing signal transduction. The aim of this paper is to describe the molecular mechanisms of scaffolding, i.e. the principles by which scaffold proteins drive a specific response of the cell. Since similar scaffold proteins are found in many species, they evolved according to the purpose of each organism. This means they require adaptability. In the usual description of the mechanisms of scaffolding, scaffold proteins are considered as reactors where molecules involved in a cascade of reactions are simultaneously bound with the right orientation to meet and interact. This description is not realistic: (i) it is not verified by experiments and (ii) timing and orientation constraints make it complex which seems to contradict the required adaptability. A scaffold protein, Ste5, is used in the MAPK pathway of Saccharomyces Cerevisiae for the cell to provide a specific response to stimuli. The massive amount of data available for this pathway makes it ideal to investigate the actual mechanisms of scaffolding. Here, a complete treatment of the chemical reactions allows the computation of the distributions of all the proteins involved in the MAPK pathway when the cell receives various cues. These distributions are compared to several experimental results. It turns out that the molecular mechanisms of scaffolding are much simpler and more adaptable than previously thought in the reactor model. Scaffold proteins bind only one molecule at a time. Then, their membrane recruitment automatically drives specific, amplified and localized signal transductions. The mechanisms presented here, which explain how the membrane recruitment of a protein can produce a drastic change in the activity of cells, are generic and may be commonly used in many biological processes.

Kinetic insulation as an effective mechanism for achieving pathway specificity in intracellular signaling networks

Intracellular signaling pathways that share common components often elicit distinct physiological responses. In most cases, the biochemical mechanisms responsible for this signal specificity remain poorly understood. Protein scaffolds and cross-inhibition have been proposed as strategies to prevent unwanted cross-talk. Here, we report a mechanism for signal specificity termed "kinetic insulation." In this approach signals are selectively transmitted through the appropriate pathway based on their temporal profile. In particular, we demonstrate how pathway architectures downstream of a common component can be designed to efficiently separate transient signals from signals that increase slowly over time. Furthermore, we demonstrate that upstream signaling proteins can generate the appropriate input to the common pathway component regardless of the temporal profile of the external stimulus. Our results suggest that multilevel signaling cascades may have evolved to modulate the temporal profile of pathway activity so that stimulus information can be efficiently encoded and transmitted while ensuring signal specificity.